QC 35 
.D7 

Copy 1 


LABORATORY EXERCISES 

IN ■ 


PHYSICS 


BY , 

CHARLES E. DULL 

SOUTH S.IDE SIGH SCHOOL, NEWARK, N, J. 
AND 

THE NEWARK, N. I. SCHOOL OF TEiCHNOLOGT 


....School. 

Room.... 





NEW YORK 

HENRY HOLT AND COMPANY 





















PREFACE 


QC sg- 

.I31 


Since it is quite impossible to select a list of experiments which all teachers of physics 
consider fundamental, it becomes necessary to include in any laboratory manual more experi¬ 
ments than the average student can perform in the time usually allotted to laboratory 
physics. In this manual an attempt has been made to include those experiments which form 
the back-bone of a well-balanced course, and enough supplementary material to meet the 
demands of teachers who wish to vary the laboratory course. While the manual is elastic, 
it meets the requirements of the College Entrance Board and of the Syllabi of the various 
states. 

Although this manual is designed to accompany the Essentials of Modern Physics, a 
text-book by the same author, yet the order can be varied to fit any modern text. For the 
most part the apparatus needed is simple and inexpensive. For use in certain experiments, 
coefficient of linear expansion for example, various types of apparatus are in common use. 
It is impossible to include a method which is suitable for every type of apparatus in such 
cases. Some alternative methods are included, and blank sheets are appended to permit 
variation of method. 

To prevent waste of time in the laboratory is a problem that the science teacher must 
face. Some students work rapidly and record results quickly. Many spend entirely too 
much time in writing up experiments. The loose-leaf manual is a time-saver for both student 
and teacher. Many teachers have come to the conclusion that the advantage which the 
student gains from writing laboratory directions does not pay for the extra time spent. The 
large number of teachers who have tried the loose-leaf type of manual are firmly convinced 
that such a manual has the following advantages; (1) The pupil can perform a larger number 
of experiments; (2) More time is available for careful observation and thoughtful conclusion; 
(3) As a permanent record the manual is worth much more to the student than a note-book 
which contains only an abstract of the method; (4) The teacher with large classes can review 
his note-books more carefully and more rapidly. 

Mr. Roger B. Saylor has kindly read all the manuscript. For the helpful suggestions 
which he offered, the author wishes to express his appreciation. He also desires to thank 
Aliss Eliza1)eth Kent, of South Side High School, for her assistance with certain drawings 



CONTENTS 


Prei-’ace. 

General Suggestions 
Curve Plotting . . . . 
Significant Figures . . 
Reading Scales . . . . 
Electrical Instruments 


V , 


pagi 

iii 

1 

1 



3 

4 

5 


Experiments 

1. (a) To measure the length of a table in centimeters and in inches 

(6) To study the relation between the English and the Metric units of length. 7 

2. To find the volume of a regular solid. 9 

3. To find the volume of an irregular solid . 11 

4. (a) To learn how to use a trip, or platform balance 

(b) To find the weight of one cubic centimeter of water. 13 

5. To find the density of certain solids. 15 

6. To show that Ikiuid pressure is proportional to its depth and its density. 17 

7. To show that the loss of weight of an object in water is exactly equal to the weight of the water displaced . 19 

8. To study the principles of flotation, and the relation between the density of a body and the fractional 

part of its volume which is submerged as it floats in water. 21 

9. (a) To find the specific weight of heavy solids 

(h) To find the specific weight of a solid lighter than water. 23 

10. (a) To find the specific weight of liquids by the use of the pycnometer, or specific weight bottle 

(b) To find the specific weight of liquids by the loss of weight method 

(c) To find the specific weight of liquids bv the hydrometer method 

(d) To find the specific weight of liquids by Hare’s method. 2.5 

11. To find the weight of one liter of air at room temperature and pressure . 29 

12. To show how the volume of a given mass of gas varies with the pressure it sustains. 31 

13. To show that the distortion of matter is proportional to the stress, within the limits of perfect elasticity 33 

14. To measure the tensile strength of various materials. 37 

15. (a) To find the resultant of two forces acting at an angle 

(b) To show that a third force which produces equilibrium with two forces is equal and opposite to 

their resultant. .39 

16. To show how a force may be resolved into its components. 41 

17. (a) To show that the equilibrant of two parallel forces is equal to their sum 

(b) To show that the equilibrant of two parallel forces must be between the two, at their center of 

moments 

(c) To show that the forces are inversely proportional to the length of the arm upon which they act . . 43 

18. To study the laws of the pendulum and to find the value of g, the acceleration due to gravity .... 47 

19. To find the coefficient of sliding friction, and to compare .sliding friction with rolling friction .... 51 

20. To studv the three classes of levers . 53 

21. To show that a lever behaves as if all its weight were concentrated at its center of gravity. 55 

22. («) To study the mechanical advantage of the fixed and the movable pulley and of pulley systems 

(5) To find the efficiencj^ of the pulley.. 57 

23. To detei-mine the mechanical advantage of the inclined plane. 61 

24. To test the fixed points of a Centigrade thermometer . 63 

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Expekiments page 

25. To measure the coefficient of expansion of certain metals .. 65 

26. To find the coefficient of expansion of gases. 67 

27. To show that the number of calories lost by a hot substance added to a colder one equals the number of 

calories gained by the latter. 69 

28. To find the specific heat of some solid. 71 

29. To find the melting point of certain crystalline solids . 73 

30. To find how many calories of heat are needed to melt one gram of ice. 75 

31. To show how a change of pressure affects the boiling point of water. 77 

32. (a) To show how a change of pressure affects the boihng point of water (Alternative) 

(b) To show the advantage of closed vessels for cooking purposes. 79 

33. (a) To find the boiling point of certain liquids 

(b) To show the effect of dissolved salts on the boiling point of a liquid 

(c) To show how mixing liquids affects the boiling point . .. 81 

34. To find how many calories are required to vaporize one gram of water without change of temperature 83 

35. (a) To find the cost of heating one quart of water from room temperature to the boiling point with a 

gas burner 

(6) To test the efficiency of a gas burner under actual working conditions . 85 

36. (a) To find the dew point of the air in the room 

(b) To determine the relative humidity of the air in the room. 89 

37. To show how convection currents are set up in liquids. 93 

38. To study radiators and the rate of coohng . .. 95 

39. To determine the velocity of sound in air at room temperature. 97 

40. To find the vibration rate of a tuning fork. 99 

41. To show how the vibration rate of a string is affected (o) by its length; (6) by its tension.101 

42. To measure the candle power of several different types of incandescent lamps.105 

43. (a) To show that the angle of reflection of fight is equal to the angle of incidence 

(b) To show how images are formed by plane mirrors.109 

44. To measure the index of refraction of a ray of fight passing from a piece of plate glass into air ... 113 

45. To find the index of refraction of a ray of fight passing from air into water.115 

46. To find the index of refraction of a ray of fight passing from air into water (Alternative method) . . 117 

47. (a) To find the focal length of a double convex lens 

(b) To show how images are formed by convex lenses 

(c) To show the relation between the size of object and image .119 

48. To find the magnifying power of a double convex lens. 123 

49. (a) Study of the compound microscope 

(b) Study of the astronomical telescope .125 

50. (a) To learn how to make a magnet (b) To find what materials are attracted by a magnet (c) To 

show polarity and its effect (d) To learn what materials are transparent to magnetism (e) To 
study induced magnetism.129 

51. To make permanent charts of the fines of force about magnets.133 

52. To make a voltaic cell and to study its action and its defects.135 

53. (a) To show that the voltage of a cell depends only upon materials used in its construction 

(b) To show that the amperage varies with the materials, the size of the plates, and the distance be¬ 
tween them.139 


(bj To learn what grouping gives the highest amperage; (1) when the external resistance is large; 

(2) when the external resistance is small.141 

55. To measure the resistance of conductors by the voltmeter-ammeter method.143 

56. To measure the resistance of conductors by the Wheatstone bridge method.147 

57. To measure the resi9* nee of conductors joined (1) in series; in parallel, or multiple.151 

58. (a) To show hoy -n increase in temperature affects the resistance of metallic conductors 

(b) To find the temperature coefficient of the resistance of some cell.153 

59. To show how the current is distributed over the branches of a divided circuit.155 

60. To measure the internal resistance of a cell (a) by the voltmeter-ammeter method; (b) by the reduced 

deflection method.157 

iii 








































Experiments 

61. To show that the fall of potential along a conductor is proportional to the resistance. 

62. To study the effects of the magnetic field which is set up around vertical and horizontal conductors . 

63. To study the electro-magnet. 

64. To study the telegraph sounder and the electric bell as applications of the electro-magnet . 

65. (a) To find the cost of heating one quart of water from room temperature to the boiling point with an 

electric heater 

(6) To test the efficiency of an electric heater under actual working conditions. 

66. (a) To compare the efficiency of carbon and tungsten lamps 

(5) To study series and parallel wiring. 

67. (a) To study the electrolysis of water. (6) To show the relation of the electrolysis of water to the 

storage cell. 

68. (a) To show how an object may be plated with copper, (b) To find out how much copper one ampere of 

current will deposit per second . 

69. To show how a magnet may induce a current in a conductor moving through a magnetic field . . . 

70. To study the principle of a simple electric motor. 

71. To test the efficiency of a small direct current motor. The use of the Prony brake. 

Appendix Tables. 


PAGE 

159 

161 

165 

167 


171 

175 

179 

183 

185 

189 

191 

195 











LABORATORY EXERCISES IN PHYSICS 


GENERAL SUGGESTIONS 

Preliminary. Read the entire experiment carefully before coming to the laboratory. 
The purpose of the experiment tells you what you are expected to learn, to observe, or to do. 
The introductory note is intended to explain the apparatus used, to clarify the problem pre¬ 
sented, and to show the relation of the experiment to every-day affairs. 

Temporary Notes. Having read the experiment before entering the laboratory, the 
student should proceed at once to assemble his apparatus, and to obtain his data. All the 
data should be entered in a temporary note-book. After the results have been calculated, 
they should be O. K’d by the instructor. Both the calculations and the data should then be 
copied in the permanent note-book. 

Calculations. In the permanent note-book the mathematical results may be indicated 
only. For example, the volume of a cylinder 4 in. long and 6 in. in diameter is indicated 
as follows: 3.142 x (3)^ x 4 in. = 113.1 cu. in., the volume. 

Use decimal fractions exclusively in all your laboratory work. Call a scant eighth a 
tenth, a big eighth or a scant quarter two tenths, a big quarter or a scant three eighths three 
tenths, and a big three eighths or a scant half jour tenths. 

Unless otherwise directed the Metric System is to be used for both measurements and 
weighings. 

Conclusions. Faulty conclusions often arise from incorrect observations, or from failure 
to understand some part of the experiment. Read all instruments with the greatest possible 
accuracy, and then compare the purpose of the experiment with your observations and data 
before attempting to draw conclusions. “ Think ” is an excellent motto. 

Questions and problems. Answer each question completely. After you have solved a 
problem, ask yourself the question, “ Is the answer a reasonable one? ” On a final exami¬ 
nation paper a student figured a monthly electric light bill for a private family at $22,500. 
Would the customer be apt to consider such a bill a reasonable one? 

CURVE PLOTTING 

Curves are often plotted to show to the eye the relation between two quantities which 
are so connected that any change in one of them is accompanied by a corresponding change 
in the other. We find that the laws of physics may often be represented graphically. In 
liquids, for example, the pressure increases with the depth. The volume which a gas 
occupies decreases as the pressure increases. 


1 


Suppose we find experimentally that a force of 5 gm. stretches a spring 1 cm, A force 
of 10 gm. stretches the same spring 2 cm.; of 15 gm., 3 cm.; of 20 gm., 4 cm.; of 25 gm., 
5 cm.; of 30 gm., 6 cm.; of 35 gm,, 7 cm,; and of 40 gm., 8 cm. 

These numbers may be used as' coordinates in plotting a curve. On a sheet of cross- 
section paper draw a horizontal line XX' and a vertical line YY' as axes from which distances 
are to be measured. See Fig. 1. The point 0 is the origin of the curve. The horizontal 
distances measured from the YY' axis are called abscissas. If the number is positive, they 
are measured to the right of the YY' axis. The vertical distances measured from the XX' 

axis are called ordinates. Positive quantities are 
measured upward from the XX' axis, and negative 
quantities downward. 

In using the above coordinates for plotting a 
curve, suppose we let the distances to the right of 
the YY' axis represent the increases in the length 
of the spring, and the varying forces used to pro¬ 
duce this increase be represented by the distances 
above the horizontal axis XX'. 

We may choose any convenient nmnber of 
small spaces to represent one unit, or several units 
may be represented by one small space. Some- 
tunes it is more convenient to use a different unit 
to represent each magnitude. In this case let us 
use one small horizontal space to represent 1 cm., 
and one small vertical space to represent 5 gm. In 
Fig. 1, the point (a) represents the two coordinates, 
1 cm. and 5 gm., since it is 1 small space to the right 
of the axis YY' and 1 small space above the XX' 
axis. In a similar manner we locate the point (6) to represent 2 cm. and 10 gm. The 
other coordinates are represented by (c), (d), (e), (/), {g), and Qi) respectively. Aline 
drawn through all these points represents a curve of direct 'proportion. It is a straight line, 
since one factor increases as the other increases. 

We may plot another curve, using the following figures as coordinates: 

AB AB AB AB 

50 4 30 6.67 10 20 5 40 

40 5 20 10. 6.67 30 4 50 

Let us use one small space to represent 4 units. The first point (a) of the curve is found 
by counting one small space to the right of YY' axis and 12.5 small spaces above the axis 
XX'. Similarly, we locate (6), (c), (d), (e), (/), {g), and {h), and draw a smooth curve 
through all these points. See Fig. 2. This curve is called the curve of inverse proportion. 

If we have given one number of a pair of coordinates, we may use the graph or curve 
to find the other number. For example, suppose we have given the first number 8 of a pair 

2 



Fig. 1 


























of coordinates. We find that two small spaces to the right of the YY' axis will intersect the 
curve at a point (s), 6.25 spaces from the XX' axis. But since (s) is-6.25 spaces from the 
horizontal axis, then the other coordinate is 4 x 6.25, or 25. 


SIGNIFICANT FIGURES 

The student often wastes valuable time in the laboratory by carrying decimals beyond 
the limit of accuracy of the instrument used for making measurements. He should carry 
one doubtful figure in making calculations and drop any other figures which are not signifi¬ 
cant. Errors may be due to imperfections in 
the apparatus, to what is called “ personal 
equation,” or to careless observation. By “ per¬ 
sonal equation ” we mean merely prejudice. For 
example, a preconceived idea may lead to inac¬ 
curacy. Students frequently get the idea that 
warm water rises higher by capillarity than cold 
water, and make readings that would indicate this, 
whereas cold water actually rises higher than 
warm water. Errors due to “ personal equation ” 
may be eliminated to a large extent by using 
great care at all times. The student must not get 
the habit of ascribing errors which are due to care¬ 
lessness to poor apparatus or to faulty methods. 

When several readings are taken, it is probable 
that some of the errors due to observation will be 
plus and others minus. For that reason, the aver¬ 
age of several trials is much more likely to be 
correct than a single trial. Suppose the student 
uses an ordinary Metric ruler to measure the length and diameter of a cylinder, estimating 
to tenths of the smallest scale division. When estimating to tenths of a millimeter an error 
of two or three tenths of a millimeter is possible. Therefore all the figures in the following 
columns which are printed in bold type may be considered doubtful: 


Length 

Diameter 

7.84 cm. 

3.44 cm. 

7.86 

3.45 

7.88 

3.47 

7.85 

3.48 

7.82 

3.47, 

7.85 

3.45 

6)47.10 

6)20.76 

7.85 

3.46 



y 

















■ -( 

% 
















































b 































1 

\ 
















V 
















Vs 

















■ 















A 

















\ 

















V 



f 





h 



X 


0 











-t- 


X' 



















y' 















Fig. 2 


3 











































If the first doubtful figure is zero, it should be retained, since the zero gives an idea of 
the exactness of the preceding figure. 

In one of the first experiments the student will be asked to measure a cylinder and 
compute its volume. He may use the following method: 

Volume = or 

4 

The radius is 1.73 cm. 



1.73 

1.73 

2.9929 

3.1416 

9.40255464 

7.85 


519 

1211 

1 73 

179574 

29929 

119716 

4701277320 

7 522043712 

65 81788248 


2.9929 

29929 

8 9787 

9.40255464 

73.8100539240 


Such a method requires a great deal of time and the chances for making 
very much greater than by the use of the following method. Furthermore, 
much greater degree of accuracy than can be possibly obtained. 

a mistake are 
it indicates a 


1.73 

2.99 

9.39 

1.73 

3.142 

7.85 

519 

598 

4695 

1 211 

1196 

7 512 

1 73 

299 

65 73 

2.99** 

8 97 

9.39*** 

73.7*** 


Whenever we multiply a number by a doubtful figure, all the figures in the partial 
product are doubtful. By using the second method, we drop a large munber of doubtful 
figures and save much time. The volume' 73.7 c.c. is just as accurate as the volume 73.8 c.c., 
since the last figure in each is obtained by an estimate. 

In all his laboratory work, the student should use only significant figures. Only the 
first doubtful figure and those preceding it are significant. 


READING SCALES 

Generally the smallest divisions on any graduated scale are not numbered. With a 
spring balance of 250-gm. capacity, for example, there are no numbers between the zero 
mark and the 50-gm. division. Since the space between these divisions is sub-divided into 
five equal parts, each small mark must represent a 10-gm. sub-division. 

In reading thermometers, voltmeter and ammeter scales, etc., the student should count 
the number of divisions between consecutive numbers, and then divide the difference between 

4 















such numbers by the number of divisions. The quotient is equal to the value of the smallest 
scale division. 


PER CENT OF ERROR 

With the measuring instruments ordinarily used in high school laboratories, perfect 
results are quite impossible. For this reason no student should feel that he is expected to 
find the ‘Toss of weight” of a block of wood exactly equal to the “weight of the water it 
displaces.” An error of several grams is permissible. The student should remember that the 
gram is a very small weight, the weight of an ordinary nickel being only 5 gm. 

Sometimes the actual error is small, and in other experiments it is fairly large. An error 
of 1 in. in measuring a table is unpardonable, but an error of 3 ft. in finding the velocity of 
sound per second is not too large. 

The accepted value is generally the average of a large number of trials taken by trained 
observers using high-grade instruments. Even the authorities do not always agree. For 
example, the heat of vaporization is given by the various authorities at values anywhere 
between 535 and 540. Strive for the best results and make an effort to improve in accuracy, 
but be honest with yourself in all your results. 

Suppose a table is 96 in. long and a careless student obtains a value of 95 in. His 
actual error is 1 in. His per cent of error equals 1/96 X 100, or 1.04%. If the accepted 
value for the velocity of sound is 1120 ft. per secondj^ and a student gets 1123 ft. per second 
as a result of his experiment, his actual error is 3 ft. While this may seem large, his per cent 
of error is 3/1120 X 100, or 0.26%. To find per cent of error, divide the actual error by the 
accepted value, and multiply the quotient by 100. 


ELECTRICAL INSTRUMENTS 

Cheap electrical instruments are so inaccurate that they are almost worse than useless. 
For the majority of experiments, commercial instruments may be used, and a few high-grade 
instruments to be used by a group of students will be found no more expensive and much 
more satisfactory than cheap instruments for each individual student. 

While electrical instruments are always made as nearly “fool-proof” as possible, yet the 
greatest care must be used to avoid over-loads. The student should bear in mind that the 
heating effects increase as the square of the amperage increases. It is a good idea to have 
a fuse plug in all electrical circuits. The capacity of the fuse must of course be less than 
that of the instrument itself. A knife switch which can be opened quickly should also be 
connected in the circuit. 

Voltmeter. For many experiments the voltmeter is more satisfactory than the galvano¬ 
meter. For that reason many of the experiments in this manual list the voltmeter in prefer¬ 
ence to the galvanometer. For very accurate readings a voltmeter of as low a range as 
possible should be selected. For example, when only a couple of Daniell cells are used, a 
voltmeter having a range of from 0 to 3 volts will give more accurate readings than one of 
higher range. For use on a lighting circuit, a voltmeter must have a range of from 0-150 

5 


volts. A voltmeter is always connected in parallel across a circuit or any part of the circuit 
whose fall of potential is to be measured. 

Ammeter. The commercial type of ammeter generally consists of a coil pivoted between 
the poles of a permanent magnet. (Movable coil type.) Since its resistance is very low, a 
shunt is connected across its terminals to prevent the instrument from being “burnt out." 
The instrument may have different shunts to give varying ranges. 

Ammeters are joined in series in a circuit. Very great care must be used before con¬ 
necting an ammeter in a circuit to see that the amperage does not exceed the range of the 
instrument. A rheostat may be connected in series with the ammeter in a circuit, and then 
the resistance can be gradually cut out until the desired amperage is obtained. 

If an ammeter has different shunts, always connect first with the binding posts which 
will give the highest range. For example, if one shunt gives a range of from 0-25 amperes, 
and a second one a range of from 0-5 amperes, the one giving the highest range should 
be tried first. Then if the amperage is less than 5, the other shunt may be used to secure 
greater accuracy. Never connect an ammeter in shunt with any other instrument. 

Galvanometers. For Wheatstone bridge work and for testing induced currents a gal¬ 
vanometer is desirable. The apparatus companies are making galvanometers having the 
D’Arsonval movement, but the coil is mounted on jeweled bearings instead of being suspended 
by means of a wire or ribbon. These instruments are very satisfactory for student use, since 
there are no broken suspensions. Since a galvanometer is not protected either by a resistance 
coil in series or by a shunt across its terminals, only a very small current may be used safely. 
The instructor may direct that a resistance coil or a shunt be used with the instrument. 

Rheostats or Resistance Coils. A rheostat may be used in a circuit to increase the 
resistance and thus reduce the amperage, or to protect certain instruments. It may be 
graduated so that it can be used as a measuring instrument. In such cases it is made of wire 
which has a high resistance, but a very low temperature coefficient. While a resistance box, 
or graduated rheostat, is affected to only a small degree by an increase in temperature, yet 
care must be taken not to use enough current to heat the coils unduly. Apparatus makers 
usually state the maximum capacity of each resistance box. The terms rheostat and resistance 
box (or coils) are used interchangeably, but in this manual the term resistance box {or coils) 
w’ill be used to designate measuring instruments, and the term rheostat to designate any 
resistance added to reduce the amperage. 


6 


Laboratory Exercises in Physics NAME_ 

Chaeles E. Dull 

Copyright, 1923, by Plenry Holt and Company 

DATE _ 


EXP. 1 — MEASUREMENT 


Purpose, (a) To measure the length of a table in centimeters and in inches. 

(b) To study the relation between the English and the Metric units of length. 

Apparatus: Meter stick; rectangular wooden block; needle or pin. 



Note. Many students are apt to regard lightly an experiment in direct measurement. 
Measuring instruments are used, however, in many of the experiments in physics, and con¬ 
siderable practice is needed to enable one to read instrmnents with precision. In all cases 
the student should strive to attain the greatest accuracy. This experiment aims to familiar¬ 
ize the student with the Metric System, which is the official system used in nearly all civilized 
countries except Great Britain and the United States. In the latter countries it is used for 
scientific work almost exclusively. On account of its simplicity, the Metric System is coming 
into extensive use in many of our factories. If a mechanic uses the Metric System long 
enough to become familiar with it, he is very reluctant to discard it for the more cumbersome 
English System. 

Cautions. In all measurements the meter stick must be kept parallel to the edge of the table. To avoid 
incorrect readings due to parallax, the edge of the meter stick, not the flat side, should be brought into con¬ 
tact with the object being measured, as shown in Fig. 3. If the meter stick hes flat on the table, as shown 
in Fig. 4, it is possible to obtain various readings, dependent upon the position of the eye of the observer. 
The reading obtained when one looks along the perpendicular BO is correct. Readings taken when the eye 
is at other positions, at A or C for example, are incorrect. 

Method. Hold the wooden block firmly against the end of the table so one edge of the 
block extends about one inch above the table. Lay the meter stick on the table (see caution) 
and slide it along until its zero end is in contact with the wooden block. If the table is more 
than a meter long, use a pin or needle to mark the position of the other end of the stick. 
When you reach the other end of the table, use the wooden block as before to find the exact 
position. If in your final reading the pin does not coincide wdth a scale division (millimeter), 
estimate the value in tenths of a millimeter (hundredths of a centimeter). Record your 

7 































readings in centimeters. Repeat the measurement, beginning this time at the opposite end 
of the table. Why? 

If your results are in close agreement, two trials are sufficient. Consult your instructor to 
learn whether a third trial is necessary. 

Repeat the experiment, using the English scale of the meter stick. It is better to use 
30 or 36 inches instead of the full length of the stick, since errors might arise from the 0.37 
inch fraction at the end. Record your results in inches and tenths. Since students generally 
use common fractions in preference to decimals, they may find the use of decimals in physics 
a little more difficult at first; after a very httle practice, the use of decimals throughout will 
prove a great time saver. The quarters and eighths of a scale division may be used as fol¬ 
lows: Call a scant eighth, a tenth, a big eighth or a scant quarter, two tenths; a big quarter, 
thi’ee tenths; and a big three eighths or a scant half, four tenths. Since the second place is 
only an estimate, there is no advantage in carrying one eighth or three eighths beyond two 
decimal places. In fact, decimals never need be carried beyond the limit of accuracy of the 
measuring instrument. 

All your results should be tabulated in the accompanying table. Using the average 
measurements in each system, compute the value of one inch in centimeters. Work out all 
your calculations and problems on scrap paper, but indicate all your mathematical processes 
and results in your note-book. For example, if you are finding the volume of a box 18 in. 
long, 12 in. wide, and 10 in. deep, you would indicate as follows: 

18 X 12 X 10 in. = 2160 cu. in., or 1.25 cu. ft. 

Data. 


Trial 

Length in centimeters 

Length in inches 

First 



Second 



Third 



Average 




Conclusion: One inch equals . centimeters. 

Calculations: 

Problems. 1. A desk is 2 ft. long and 16 in. wide. Find its length and breadth in 
centimeters. Find its area in square inches. In square centimeters. 


2. Find the value of 100 yards in centimeters. In meters. 


8 












Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 


DATE_ 

EXP. 2 —MEASUREMENT 


Purpose. To find the volume of a regular solid. 

Apparatus: Section of a meter stick; vernier caliper; rectangular wooden block, about 3x3xl.5 inches; 

regular cylinder, preferably of brass or aluminum (about 2 or 3 inches long and 1 
or 1.5 inches in diameter). 



Fig, 6 



Fig. 7 


Note. ^ When using a meter-stick or a yard-stick, it is necessary to estimate the smallest 
scale divisions. By the use of a vernier caliper, more accurate measurements can be made. 
See Fig. 5. The vernier consists of two scales; one is fixed, and the other is so arranged 
that it may slide along the fixed scale. In the metric vernier caliper, the fixed scale is 
divided mto^ centimeters and millimeters (tenths). Nine millimeters on the sliding scale 
are divided into ten equal parts. Therefore one of these divisions equals 0.9 mm. Compare 



Fig. 6. As we move the slide scale B to the right until its Jirst division coincides with the 
one millimeter mark on A, we move it exactly 0.1 mm., or 0.01 cm. Sliding the scale to 
the right until its second division coincides with the 2 mm. mark on A moves the slide 
0.2 mm., or 0.02 cm. Moving the scale to the right 0.03 cm. brings its third division 
opposite the three millimeter mark on A, and so on. That division on the slide scale which 
coincides with a division on the fixed scale reads hundredths of centimeters. Suppose the 
scale is moved to the right to the position shown by the dotted lines. The reading is 

9 












































made as follows: The zero of the slide scale shows that the value is more than 1.5 cm., and 
less than 1.6 cm. To read hundredths we locate that division on the slide scale which coin¬ 
cides with a division on the fixed scale. As indicated by the arrow, it is No. 6 in this 
case. Therefore the reading is 1.56 cm. In reading a vernier scale, we read centimeters 
and tenths on the fixed scale, and hundredths on the slide scale. 

When a vernier is graduated in the English system, the fixed scale may be divided into 
inches and tenths, and the vernier reads hundredths. Sometimes the fixed scale is divided 
into inches and sixteenths, and the vernier reads 128ths. 

Method. Find the length, breadth, and thickness of the block in centimeters, using 
the vernier caliper. Repeat the measurement, placing the caliper at a different position on 
the block. From the average, compute the volume of the block in cubic centimeters. If a 
vernier caliper is not available, a section of meter stick may be used. 

Next measure the length and diameter of the cylinder. If a meter stick is used for this 
measurement, the diameter of the cylinder may be found by placing rectangular blocks on the 
sides of the cylinder as in Fig. 7, and measuring the distance between them. To compute the 
volume of the cylinder, multiply 0.7854 times the diameter squared by its length. Volume 
= IttD^L, or ttR^L. 

Data. 


Trial 

Length of 
block 

Breadth of 
block 

Thickness 
of block 

Length of 
Cyiinder 

Diameter of 
Cylinder 

First 






Second 






Average 







Volume of block No.is . c.c. Volume of cylinder No.is .c.c. 

Calculations: 


Problems. 1. A glass cylinder 30 cm. long has an internal diameter of 5 cm. How many 
cubic centimeters does it hold? 


2. Read the vernier scale on the laboratory barometer. Ask the instructor to verify 
your reading. 


10 













Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 3—MEASUREMENT 


Purpose. To find the volume of an irregular solid. 

Apparatus: Cylindrical graduate, 100 or 250 c.c. capacity; irregular piece of metal, marble, coal, 
trap rock, or other non-porous solid; beaker; thread. 

Note. If a solid is irregular, we can not measure its volume directly, as we did in 
Exp. 2. It is possible to find its volume indirectly, because two bodies cannot occupy the 
same place at the same time. A solid lowered into a liquid until it is completely submerged 
displaces its own volume of liquid. By measuring the volume of liquid displaced, we can find 
the volume of the solid. 



Caution. Liquids that wet glass have slightly concave surfaces; the 
liquid is lifted shghtly at the surface at all points where it comes into 
contact with the glass. In reading the level of such hquids it is customary 
to read to the bottom of the dark surface line, or the meniscus. In Fig. 8, 
the correct reading is 40 c.c. The eye at E must be so placed that the 
line of vision is perpendicular to the graduated scale. Liquids like mercury 
which do not wet glass have convex surfaces. The correct reading of their 
surface levels is the top of the meniscus. 


Method, (a) FiU the graduated cylinder about two fifths full of water and read the 
water level exactly, using the precautions given for reading liquid levels. Tie one end of a 
piece of strong thread to the solid whose volume is to be found and lower the solid into the 
cylinder until it is completely submerged. Again read the water level. The difference be¬ 
tween the two readings equals the volume of the solid. 

(6) Repeat the experiment, using a different volume of water. Whyf 


(c) If the instructor so directs, repeat the experiment, using the cylinder measured in 
Exp. 2. -Thus the student may compare the direct and indirect methods of measurement. 


11 






















Data. 


Trial 

First reading 

Second reading 

Voiume 

First 




Second 




Third 




Fourth 





Average volume of solid No. is . c.c. 

Average volume of cylinder No.is . c.c. (Indirect) 

Volume of cylinder from Exp. 2 is . c.c. (Direct) 

Questions. 1. How could you find the volume of a lump of rock salt by such an in^ 
direct method? 


2. Can the volume of a porous solid be found by this method? If so, how would you 
proceed? 


3. Which is the more convenient method for finding the volume of a cylinder, the 
direct or the indirect? Which do you think is more exact? 


12 














Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 4 —WEIGHT 


Purpose. (a) To learn how to use a trip, or platform, balance. 

(b) To find the weight of one cubic centimeter of water. 

Apparatus: Trip balance; set of weights; thermometer; beaker, 100 cc.; tumbler, or extra beaker; 
burette; burette clamp and stand; one-lb. weight. 

Note. In a laboratory course in physics, many weighings will have to be made. In 
some cases a spring balance may be used. Such a balance is so easy to use that little or no 
explanation is necessary. Weighings made by a trip balance are more accurate, but more 
time is required to make the weighings. Fig. 9 shows a type of balance that is much used in 

physical laboratories. The center of 
the beam and the pans themselves rest 
upon knife-edged bearings. Generally 
there is a pointer attached to the beam 
to show when the two pans are level. 

In using such a balance, the stu¬ 
dent should first see that the slide 
weight P is at the extreme left, or at 
zero. Then he may touch one of the 
pans lightly to set the balance swinging. 
The pans should move far enough so 
the pointer will swing at least two or 
three spaces to either side of the center. 
If it swings farther to one side than to 
the other, the screw S may be adjusted 
until the pointer moves just as many spaces to the left as to the right. The scales are now 
“ balanced.” The object to be weighed is then placed on the left pan of the balance. Select a 
weight which seems to be slightly heavier than the object to be weighed and place it on the 
right scale pan. If it is heavier, remove it and try the next smaller weight. If this weight 
is lighter than the object, continue to add weights to the right scale pan, trying weights 
successively from the larger to the smaller, until the last weight added is the ten-gram weight. 
Then the slide weight may be used; it should be moved to the right until the pointer swings 
the same number of spaces to the left as to the right. It is unnecessary to wait for the 
pointer to come to rest. The weight of the object equals the sum of all the weights on the 
right pan plus the weight represented by the slide P. The instructor may prefer to weigh 
some object for each laboratory section to demonstrate the proper use of the balance. 



13 



















Cautions. The balance must be level, and the pans free from dust or foreign matter. 

Beakers and similar objects to be weighed must be dry on the outside before they are placed on the 
pan of the balance. 

If a weight is missing from the box, or if your balance is not working properly, notify the instructor 
before you begin a weighing. 



Data. 


Be careful not to jar the balances when adding or removing the heavier weights. 
Such jarring dulls the knife-edges and makes the balance less sensitive. It may be 
avoided by supporting the pan with the left hand while objects are being added or 
removed. The object to be weighed and the heavy weights should be placed in the 
center of the scale pan. 

See that all weights are returned to their proper place in the box. If no weights 
were missing from the box when the weighing was begun, the student may check 
his results by finding the sum of aU the weights from the vacant spaces in the box. 

Method, (a) Weigh a clean, dry beaker, observing all the direc¬ 
tions and precautions already given. 

(b) Clamp the burette in a vertical position and fill it with distilled 
water to a height of about one inch above the zero mark. Then open 
the stop-cock a little, and draw off enough water in a tumbler to bring 
the water in the burette just to the zero mark. In this manner all the 
air is expelled from the tip T as it is filled with water. See Fig. 10. 
Observe caution in Exp. 3 as you read the burette. After the burette has 
been read very carefully, draw off 80 c.c. of water into the weighed beaker. 
Read the burette accurately, and then weigh the beaker and water. 

(c) Re-fill the burette and repeat the experiment, using 90 c.c. of 
water for the second trial. In each case compute the weight of one c.c. of 
water. Take the temperature of the water and look up in Table 12 of 
the Appendix the weight of 1 c.c. of water at the observed temperature. 


Trial - 

First 

reading 

Second 

reading 

Difference 
or volume 

Weight of 
beaker 

Wt. of beaker 
and water 

Weight of 
water 

First 







Second 








Weight of one c.c. of water: 1. gm. 2.gm. 

Weight of one c.c. of water at observed temperature (t.) .gm. 


Problems. 1. Why is it better to put the object to be weighed on the left scale pan? 


2. Weigh an ordinary nickel. For what weight can it be substituted without much 

error? . 

3. Weigh a one-pound weight in grams. Compare your result with the table of Metric- 
English equivalents in the Appendix. 


14 






















Laboratory Exercises in Physics 
Charles E. Doll 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 5 —DENSITY 


Purpose. To find the density of certain solids. 

Apparatus: Trip balance; set of metric weights; solids used in Experiments 2 and 3. 


Note. Such sol’ds as lead and iron are heavy; cork and charcoal are very light. By 
these statements we mean that a given volume of each of these substances has a different 
weight. There are more pounds in one cu. ft. of lead than there are in one cu. ft. of iron. 
The weight of unit volume of a substance is called its density. The volume generally used 
in the Metric System is the cubic centimeter; in the English System the cubic foot is the 
most common unit. 

Method. If the solids used in experiments 2 and 3 are used in this experiment, it will be 
unnecessary to re-determine their volume. If the instructor desires to have other solids used, 
their volume may be found by one of the methods given. 

Weigh the block of wood and the cylinder you used in Exp. 2, and the irregular solid 
whose volume you found in Exp. 3. Knowing the weight and the volume, it is easy to find 


the weight of unit volume. In the Metric System, density equals ; in the English System, 

c.c. 

density equals - 

cu. ft. 


Data. 


Substance used 

Volume (c. c.) 

Weight (gm.) 

Density 














Problems. 1. A cubic foot of a certain sample of hard coal weighs 90 lb. How many 
tons of coal can be put in a bin 10 ft. long, 8 ft. wide, and 5 ft. high? 


2. Sand has a density of 125 lb. per cu. ft. A wagon-box is 10 ft. long, 3 ft. wide, and 
16 in. deep. Plow many pounds of sand will the box hold, if it is level full? 


15 


















Laboratory Exercises in Physics 
Chaeles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 6 —LIQUID PRESSURE 


PuEPOSE. To show that liquid pressure is proportional to its depth and its density. 

Apparatus: Graduated aluminum tube, 12 in. long, 1 in. diameter, and 1 mm. wall; shot; weights; 

tall cylinder, or 250 c.c. graduate; alcohol; salt water solution of known density; 
paraffin. 

Note. When a boat floats in water, it is pushed up by the water displaced. If the 
boat is loaded more heavily, it sinks deeper into the water. Therefore, the upward pressure 
of the water must increase with the depth. In this experiment, we shall float an aluminum 
tube, and then add weights successively, measuring each time the depth to which the weighted 
tube sinks. When a boat goes from the Mississippi River into the Gulf of Mexico, the up¬ 
ward pressure of the water becomes greater and the water line of the boat rises. The salt 
water in the Gulf is denser than the water in the River. 



Fig. 11 


DEPTH 

Method. Use as short a piece of cork as possible to close one end of the 
aluminum tube. Cut off the excess cork when the tube has been stoppered 
tightly. Add 45 gm. of shot to the tube and enough melted paraffin to hold 
the shot in place after the paraffin solidifies. Float the aluminum tube in 
water in a tall cylinder and record the depth to which it sinks. See Fig. 11. 
If the tube has been properly weighted, it will float vertically. Add a 5 gm. 
weight to the tube, and again record the depth to which it sinks. In the 
same manner, read the depth to which the tube sinks when 10, 15, 20, 25, 
30, 35, and 40 gm. are added successively. To find the effect of the weight 
alone, subtract in each case the depth to which the unweighted tube sinks 
from the depth to which it sinks after the addition of each weight. 


17 














Data. 


Trial 

Weight used 

Depth 

Effect of weight alone 

0 

Unloaded tube 



1 




2 




3 




4 




5 




6 




7 




8 





Conclusion: The pressure which a liquid exerts is 


DENSITY 

Method. Fill the tall cylinder with alcohol and float the aluminum tube in the alcohol. 
Measure the depth to which it sinks. Compare the depth to which the tube sinks in alcohol 
to the depth it sinks in water. Result? . 

Repeat the experiment by floating the tube in a cylinder of salt water of known density. 
The aluminum tube should be coated with a very thin layer of paraffin. Compare the depth 
to which the tube sinks in salt water to the depth it sinks in water. 


Conclusion: The pressure which a liquid exerts is . 

Curve. Plot a curve to show the relation between the pressure of a liquid and its depth, 
using the weights added to the tube as abscissas and the increases in depth as the ordinates. 


18 





















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 


\ 

DATE ___ 

EXP. 7 — ARCHIMEDES’ PRINCIPLE 


Purpose. To show that the loss of weight of an object in water is exactly equal to the 
weight of the water displaced. 

Apparatus; Overflow can; catch bucket; tumbler; trip balance, or spring balance; set of weights; 
« clamp for trip balance; battery jar; tliread; some solid having a volume of 100-150 c.c. 

(marble, coal, granite, metal cylinder, or loaded wooden cylinder); loaded wooden 
cyhnder, lighter than water. 



Note. In teaching a person to swim, we find it very easy to keep him from sinking, 
since he is buoyed up by the water his body displaces. Objects floating in water lose all 
their weight. Solids denser than water lose part of their weight when submerged. Archimedes 
observed that bodies lose weight when immersed in water. In Exp. 3 we learned that objects 
displace a volume of water equal to their own volume. In this experiment it will be shown 
that the loss of weight of an object in water equals the weight of the water that object 
displaces. (Archimedes’ Principle.) 

Cautions. Be sure that the heavy solid is entirely submerged, so it will displace its own volume of 
water. It must be fastened directly beneath the point of suspension of the scale pan. If the solid touches 
the sides or the bottom of the vessel while it is being weighed, the results will be inaccurate. 

19 
























Method, (a) Tie a thread several inches long to the heavy solid, and then weigh it in 
air; suspend it in the battery jar of water and weigh it when it is entirely submerged. You 
will find a little hook directly beneath the scale pan of the trip balance to which the thread 
may be attached. See Fig. 12. A spring balance may be used for the weighings, if the 
instructor so directs. The difference between the two weighings is the loss of weight of the 
solid in water. 

(b) Holding a thumb over the spout of the over-flow can, fill the can nearly full of 
water. Set it on the table, remove the thumb, and in a tumbler catch all the water that 
flows from the spout. Let ail the water rmi out that will, and throw it away; the over-flow 
can will then be full just to the spout. ^ 

(c) Weigh the catch-bucket and place it under the 
spout of the over-flow can. Slowly lower the solid into the 
can until it rests on the bottom. See Fig. 13. Catch all 
the water that overflows and then weigh the catch-bucket 
and water. Find by difference the weight of the water 
displaced by the solid. 

(d) Repeat the experiment, checking all weighings. 

(e) For a third trial, use the lighter block, which should 
be loaded so it will float vertically. The method is the 
same as before, but of course the block will not be sub¬ 
merged, but partially submerged as it floats in water. 



Data. 


Trial 

Wt. of ob¬ 
ject in air 

Wt. of ob¬ 
ject in water 

Loss of 
weight 

Wt. of 

catch-bucket 

Wt. of catch- 

bucket 
and water 

Wt. of 
water 

First 







Second 







Third 








Conclusion: 


Problems. 1. A stone weighs 200 gm. in water; its volume is 300 c.c. What is the 
weight of the stone in air? 


2. An object weighs 90 gm. in air, and 60 gm. in water. What is its volume? 

20 





































Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE- 


EXP. 8 —PRINCIPLE OF FLOTATION 


Purpose. To study the principles of flotation, and the relation between the density of a 
body and the fractional part of its volume which is submerged when it floats 
in water. 

Apparatus: Compre?sion spring balance, 250 gm. capacity; dividers; battery jar; metric ruler; 
rectangular block used in Exps. 2 and 5. 



Fig. 14 


Note. A battleship floats, despite the fact that it is made of steel 
plates from 12 to 18 in. thick. It is spread out enough to displace 
its own weight of water. For every 64 lb. of weight added to an ocean 
vessel, the vessel sinks enough deeper to displace 1 cu. ft. more of water. 
(The density of sea-water is 64 lb. per cu. ft.) If we push down on a 
floating block with a force of 1 gm., the block will sink enough deeper 
to displace 1 c.c. more of water. 

Method, (a) Fill a battery jar nearly full of water, and float the 
block upon it. If you are using the same block that you used in Exps. 
2 and 5, its weight, thickness, volume, and density as already deter¬ 
mined may be recorded. If a different block is used, it must be 
measured and weighed to find these quantities. By the aid of a pair of 
dividers, measure that part of the thickness of the block which extends 
above the surface of the water. 

(b) Placing the points of the compression balance on the center of 
the floating block, force it down beneath the surface of the water. 
Read the balance as you hold the block under water. See Fig. 14. 
Does it require any more force to hold the block 2 cm. beneath the 

surface than it does to hold it at a depth of 1 cm.?. 

Compute the number of c.c. in that portion of the block which floats 
above the surface. Compute also the number of c.c. that are sub¬ 
merged as the block floats. 


Data. 


Weight 

Thickness 

Volume 

Thickness of 
part above 
water 

Thickness of 
part sub' 
merged 

Force needed 
to submerge 
block 

No. of c. c. 
above sur¬ 
face 

No. of 
c. c. 

submerged 




j _:- 







21 































Calculations: 


Problems. 1. What fractional part of the block is submerged? How does the fractional 
part submerged compare with the density? 


2. Compare the number of c.c. that float above the surface with the number of grams 
required to force the block beneath the surface. 


3. The handle of a hammer has a volume of 1200 c.c. Its density is 0.6 gm. per c.c. 
The head of the hammer weighs 780 gm. Its density is 7.8 gm. per c.c. Will the combi¬ 
nation, hammer and handle, sink or float in fresh water? How many grams of force must be 
used to hold it just beneath the surface of the water? 


22 


I.aboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 9 —SPECIFIC WEIGHT OF SOLIDS 


Purpose. (a) To find the specific weight of heavy solids. 

(6) To find the specific weight of a solid lighter than water. 

Apparatus: Trip balance, or spring balance; set of weights; battery jar; thread; specimens of metal, 
rock, coal, etc.; blocks of paraffin, or corks coated with paraffin; sinker for light solid. 

Note. To find the specific weight of an object, we must find its density, and then divide 
its density by the density of water. We already know that we find the density of an object 
by dividing its weight by its volume. Its weight can be obtained directly by weighing it, 
but if it is irregular, we find its volume indirectly by applying Archimedes’ Principle. In 
Exp. 7 we learned that the loss of weight ” of a submerged body equals the “ weight of 
the water displaced.” Since 1 c.c. of water weighs 1 gm., then the “ loss of weight ” in grams 
exactly equals the volume in c.c. 

Method. For heavy solids. Weigh the solid in air, and then weigh it in water, sus¬ 
pending it from the hook of the balance just as you did in Exp. 7. Observe the same pre¬ 
cautions as in that experiment. The difference, or “ loss of weight,” numerically equals the 
volume. Dividing the weight in air by the “ loss of weight ” in water gives the density. 

The specific weight equals sohd same manner, find the specific weight 

density of water. 

of as many different solids as your instructor may direct. 


Data (for heavy solids). 


Material 

Weight in air 

Weight in water 

Difference 

Specific weight 
















- 






Calculations: 


23 

















Method. For light solids. Weigh the solid in air, and a sinker in water. Find the sum, 
solid in air plus sinker in water, and call the combined weight w'. The combined weight may 
be found by attaching both to the hook beneath the balance in the 
■ manner shown in Fig. 15. The sinker should next be attached to the 
solid in such a manner that both will be submerged when they are sus¬ 
pended from the arm of the balance. Weigh the solid and sinker in 
water and call their combined weight w". The difference, w' - w", is 
the buoyant effect of the water on the light solid alone, or numerically 
its volume. We find the specific weight from the formula: 

Sp. wt. = . The student will probably be astonished to learn 

w' - w" 

that the combined weight of solid and sinker in water is less than the 
weight of solid in air plus sinker in water. One needs to remember that 
the light solid acts as a float just as a piece of cork on a fish-line or a 
life preserver attached to one’s body. 

Data. 


Material 

Weight 
in air 

Wt. of sink¬ 
er in water 

Wt. of solid in 
air and sinker 
in water 

Wt. of both 
in water 

Volume 
{ \ n ' - wb 

Specific 

weight 
























Calculations: 


Problems. 1. A piece of silver weighs 62.4 gm. In water it loses 6 gm. Find the 
specific weight of silver. 


2. A block of wood weighs 80 gm. A sinker weighs 180 gm. in water; 
weigh 60 gm. in water. Find the specific weight of the block of wood. 


both together 


24 






















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 10 —SPECIFIC WEIGHT OF LIQUIDS 


Purpose. (a) To find the specific weight of liquids by the use of a pycnometer, or specific 
weight bottle. 

(6) To find the specific weight of liquids by the loss of weight method. 

(c) To find the specific weight of liquids by the hydrometer method. 

(d) To find the specific weight of liquids by Hare’s method. 

Apparatus; First method. Pycnometer; trip balance; set of weights; distilled water; alcohol; satu¬ 

rated solution of salt; solution of copper sulphate. Other liquids may be substituted 
or added. Second method. Glass bulb, or stopper; trip balance; weights; solutions 
as directed for use ivith first method. Third method. Weighted rods, 30 cm. long and 
1 sq. cm. cross-section; hydrometer jars, 12 in.; hydrometer, for light liquids; hydrom¬ 
eter, for heavy liquids; solutions as listed under first method. Fourth method. Two 

tumblers; two glass tubes, 2 ft. long and J in. internal diameter; T-tube; screw 

clamp; rubber tubing, for connections; liquids as in first method. 

Note. Several methods are in general use for finding the specific weights of liquids. By 
finding the weight of 100 c.c. of salt water, and dividing it by the weight of the same volume of 
pure water, we find the specific weight of the salt water directly. This is known as the flask 
(pycnometer), or bottle method. One floats more easily in salt water than in fresh water, 
because the salt water is heavier and has more buoyancy. If a stick floating vertically 
(hydrometer) in salt water is transferred to fresh water, it will sink farther in the latter. 
The depths to which the stick sinks in any two liquids are inversely proportional to the 
specific weights of the liquids. The “ loss of weight,” or bulb method depends upon the same 
principle. A glass bulb or stopper loses more weight in a heavy liquid than it does in a light 

one. The specific weights of two liquids are directly proportional to the losses of weight of 

an object weighed in them. The method devised by Robert Hare makes use of the fact that 
liquids rise in exhausted tubes. The lighter the liquid, the higher it will be forced by atmos¬ 
pheric pressure. The lengths of the liquid columns are inversely proportional 
to their specific weights. 

Bottle method. Weigh the dry specific weight bottle. See Fig. 16. Fill 
it with distilled water, wipe off all the water from the outside, and weigh 
again. After the water has been poured out, the bottle should be rinsed two 
or three times with the liquid of unknown specific weight, then filled with the 
liquid, and weighed. Be sure to subtract the weight of the empty flask from 
the weight of the water and flask, and from the weight of the liquid of 
unknown density and the flask. Find the specific weight of the unknown 
liquid by dividing its weight by the weight of the water. (Equal volumes.) 
Proceed in the same manner, if other liquids are to be used. 

25 



Fig. 16 










Data 


Liquid 

Weight of 
flask 

Wt. of flask 
and water 

Wt. of flask 
and iiquid 

Wt.of 

water 

Wt. of 
liquid 

Specific 

weight 























Calculations: 


“ Loss of weight ” method. Weigh the glass bulb, first in air, then in water, and finally 
in the liquid whose specific weight is to be found. Next compute the “ loss of weight ’’ in 
water, which equals the volume of the bulb. The ‘‘ loss of weight ” in the liquid of unknown 
specific weight divided by the “ loss of weight ” in water equals the specific weight of x liquid. 
Repeat, using such other liquids as the instructor may direct. 

Data. 


Liquid 

Wt. of bulb 
in air 

Wt. of bulb 
in water 

Wt. of bulb 
in X liquid 

Loss of wt. 
in water 

Loss of wt. 
in X liquid 

Specific 

weight 























Calculations: 











- 


- 

Hydrometer method. Put the hydrometer rod, weighted end 


1 






down, into the jar, and read the number of centimeters submerged. 

r-- 

i 

7-= 




7 

Fig.^ 17. Remove the rod, wipe it dry, and put it into the jar con¬ 



fj 


7" 



taining the liquid of unknown specific weight. The sp. wt. equals 







-- 

the number of centimeters submerged in water divided by the 





7 



number of centimeters submerged in the x liquid. Proceed in the 

\ 




T 



same manner to find the specific weight of such liquids as the 


) < 

* 



IT 



instructor directs. Use a commercial hydrometer to find the specific 





— 



^ weight of each liquid used. Fig. 18. 





Fig. 18 


Fig. 17 


26 


















































Data. 


Liquid 

Length (L)of 
rod submerged 
in water 

Length (LO of 
rod submerged 
in X liquid 

Specific weight 
L/k 

Specific 
weight, by 
hydrometer 


















Fig. 19 


Hare’s method. Arrange the apparatus as shown in Fig. 19. 
The tumbler A contains distilled water and tumbler B the x liquid. 
Both should stand at the same level. Carefully suck out the air 
from the tubes until the liquid in one of the tubes stands at a 
height of 30 centimeters or more. Then close the pinch-clamp 
tightly while you measure the height of each liquid column. Meas¬ 
ure from the surface of the liquid in the tumbler to the height of the 
column. Divide the length of the water column (L) by the length (L') 
of the column of x liquid. The quotient is the specific weight of 
X liquid. 


Data. 


Kind of liquid 

Length(L)of 
water column 

Length(LOof 
column of X liquid 

Specific 

weight 














27 




















Problems. 1. If a lactometer is available, test a sample of milk. The N. Y. Board of 
Health lactometer reads at least 100 in milk free from added water. After testing the milk, 
add a little water to it and test again. Record the readings. 


2, Name as many practical applications of the specific weight of liquids as you can. 


28 


Laboratory Exercises in Physics 
Chaeles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME_ 

DATE_ 

EXP. 11 —WEIGHT OF AIR 


Purpose. To find the weight of one liter of air at room temperature and pressure. 

Apparatus: Round-bottomed flask, 250 c.c. capacity; one-hole rubber stopper to flt flask; glass 
tubing; rubber tubing, heavy wall or pressure; screw clamp; balance, sensitive to 
0.01 gm.; weights; graduate; thermometer; barometer; aspirator, or air-pump; 
battery jar. 

Note. No one ever questions the fact that iron is heavju The boy wTo carries an arm¬ 
ful of wood know^s that wood has weight. The pupil with a number of books on his arm is 
conscious of the weight of paper. We do not feel the w^eight of air, but we know that smoke 
and balloons rise, or, to be more accurate, that they are pushed up by the weight of the air 
they displace. These are applications of Archimedes’ Principle to gases. In this experunent 
we shall try to find the weight and buoyancy of one liter of air. 

Caution. Do not try to use a flat-bottomed flask, as it will be crushed by the atmospheric pressure. The 
pieces of glass tubing should not be over 2 in. long. 



Method. Weigh the flask wdth stopper, screw-clamp, and 
tubing as shown in Fig. 20. Of course the flask is full of air. 
Exhaust the air, either by connecting it to an aspirator on the 
laboratory faucet, or to an air-pump. Close the screw-clamp 
tightly, and weigh the flask again. The difference between the 
two w'eights equals the w^eight of air removed. Hold the end 
of the glass tube under w^ater, open the clamp, and let all the 
water run into the flask that will. Close the clamp again while 
you remove the flask from the w^ater. Using a gi’aduate, meas¬ 
ure the number of c.c. of water in the flask and tubing. This 
is equal to the number of c.c. of air removed from the flask at 
room temperature and pressure. 

Find the weight of one c.c. of air and of one hter. Read 
the thermometer and take the barometer reading. Find the 
correct weight of 1 c.c. of air at the observed temperatm-e 
and pressure, table 6, in the Appendix. 


Fig. 20 


29 

































Weight of flask and air. 

Weight of flask. 

Weight of air. 

Volume of water (air). 

Temperature.. 

Barometer reading. 

Wt. of 1 c.c. of air... 

Wt. of 1 c.c. of air, from table in Ap¬ 
pendix. 

Error. 

Calculations. 



Problem. Find the weight of air in a room .10 m. long, 8 m. wide, and 4 m. high. One 
cubic meter equals 1000 liters. 


30 











Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 12 —BOYLE’S LAW 


Purpose. To show how the volume of a given mass of gas varies with the pressure it 
sustains. 

Apparatus: Ring stand; burette clamp; meter stick; barometer; glass tube, bent as directed 
in the method; thistle tube, drawn to point. 

Note. At sea-level the air pressure is 14.7 lb. per sq. in. By means of a compression 
pump, we can crowd 5 .atmospheres, or 5 times as much air, into an automobile tire as it 
contained at atmospheric pressure. The pressure the air exerts against the walls of the tire 
is 73.5 lb. per sq. in. When the valve is opened, the air expands again to 5 times its original 
volume. All gases are perfectly elastic. The use of steel cylinders for storing such gases as 
oxygen, hydrogen, carbon dioxide, ammonia, and acetylene (Prest-O-lite) is common. The 
gases are forced into the cylinder under a pressure of 10 atmospheres or more; they expand 
correspondingly when the valve is opened. The behavior of gases under varying pressure was 
studied by Robert Boyle, who formulated the law that bears his name. 

Cautions. The mercury column must be free from air bubbles. The height of the mercury is the vertical 
height, not the slant height. From cautions in Exp. 3, we learn that the top of the meniscus should be used 
in measuring mercury columns. Compressing a gas heats it and causes expansion. More accurate results 
can be obtained if time enough is taken between readings for the air column to cool. 


Method. Given a thick-walled glass tube 4| ft. long and not over J in. internal diameter. 
6 in. is better.) Draw it out at one end to make a short jet tube which can be easily 

sealed. Eighteen inches from this 
end bend the tube at right angles. 
Make another right angle bend 6 in. 
from the other end of the tube, but 
this bend should be at right angles 
to the plane formed by the first 
bend. See Fig. 21. This gives us a 
tube with one end turned up as the 
L-shaped portion of the tube lies fiat 
on the table. While the end D is raised a few inches, enough mercury should be added 
(use the thistle tube) at C to fill AB, and about 1 in. of AD. Next seal D so it is air¬ 
tight. As the tube lies on the table, we have a cylindrical column of air enclosed in AD 
under a pressure equal to that of the atmosphere. Measure the length of the air column in 
centimeters and record it as the original volume. The volume of a cylinder is proportional 
to its length. The barometer reading (in cm.) is the original pressure. 

31 





















While AD is kept flat on the table, lift the end B 15 or 20 cm., and clamp the tube 
firmly in position. This rotates the tube about AD as an axis. Measure the length of 
the air column to find the new volume. Measure the vertical height of the end of the 
mercury column in AB. Since the pressure upon the air has been increased by the vertical 
height of the mercury, we must add this reading to the barometer reading each time to 
find the new pressure. 

Take at least four more readings, lifting the tube at B enough each time so the 
pressure will be increased by 12 or 15 cm. For the last reading the tube AB may be held 
vertically. 

Since the volume decreases as the pressure increases, the product of the pressure and 
volume should be the same in all cases. Stated algebraically, VP = a constant. Calculate 
the product VP for all cases. Plot a curve, using the volumes as abscissas and the pressures 
as ordinates. 

Data. 


Trial 

Length of air 
column, V 

Height of 
mercury 

Total pressure of 
mercury (cm.) P 

V X P 

1 





2 





3 





4 





5 





6 






Calculations: 


Problems. 1. The volume of a dry gas is 640 c.c. when the barometer reads 78 cm. 
What will its volume be when the pressure upon it is 90 cm. of mercury? 


2. The volume of a dry gas is 230 c.c. when the pressure upon it is 70 cm. What pressure 
must be applied to this gas to reduce its volume to 100 c.c.? 


32 













Laboratory Exercises in Physics 
Chables E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 13 —HOOKE’S LAW 


Purpose. To show that the distortion of matter is proportional to the stress, within the 
limits of perfect elasticity. 

Apparatus; Jolly balance; set of small weights; torsional apparatus; rods (6 mm. square) for torsional 
apparatus. If the Jolly balance is not available, make a coiled spring by winding 
20 or 25 turns of No. 20 spring brass wire on a rod f in. in diameter. Make a hook 
at each end as in Fig. 22. 


Note. The force tending to distort any material 
upon which it acts is called a stress; the distortion 
produced is called a strain. In using an ordinary spring 
balance, we observe that the stretching of the spring 
(strain) is directly proportional to the weight applied 
(stress). If the spring is perfectly elastic, it resumes its 
original form when the stress is removed. The change in 
the form of materials under stress applies to bending, 
twisting, and compressing, just as it does to stretching. 
It applies to bars, beams, rods, wires, etc., just as it 
does to coiled springs. 

Caution. Use a support on the Jolly balance so you do not 
stretch its spring beyond the limits of perfect elasticity. Since 
the springs used with such balances have different capacities, your 
instructor will direct you what series of weights to use. 


EXTENSION. 

Method. Assemble the Jolly balance as shown in Fig. 23. Read the 
position of the pointer on the mirror scale. See that your eye is in line 
with the pointer and its image in the mirror when you read its position. 
Call this reading taken with the pan alone the zero reading. Then place 
a 1 gm. weight on the pan and read the position of the pointer. Take a 
zero reading after each trial. Proceeding in the same manner, add succes¬ 
sively 2 gm., 3 gm., 4 gm., 5 gm., 6 giu., 7 gm., and 8 gm. If the spring 
is heavy enough, make the weights 5 gm., 10 gm., 15 gm., etc., to 40 gm. 
Plot a curve, using the weights as abscissas, and the differences or elonga¬ 
tions as ordinates. The zero reading is to be subtracted from each reading 
to find the elongation. 




Fig. 23 


33 















Data. 


TRIAL 

ZERO READING 

FINAL READING 

WEIGHT 

DIFFERENCE 

ELONGATION PER QM. 

1 






2 






3 






4 






5 






0 






7 






0 







Conclusion: 


TORSION. (Group experiment.) 



Method. Clamp a steel rod in position 
in the torsional apparatus shown in Fig. 24. 
This apparatus has a vernier, which should 
be adjusted, after the pan is attached, so 
its zero exactly coincides with the zero of the 
circular protractor. Add a 100-gm. weight 
to the pan and read the vernier exactly to 
find the amount of rotation. Repeat, using 
200 gm., 400 gm., 600 gm., 800 gm., 1000 gm., 
1500 gm., and 2000 gm., respectively. 


Fig. 24 


34 






















Data. 


TRIAL 

ZERO READING 

FINAL READING 

WEIGHT 

DIFFERENCE 

ROTATION PER 

100 QM. 

1 






2 






3 






4 






5 






6 






7 






8 







Conclusion: 


Questions. 1. Does Hooke’s law apply to gases and liquids? 


2. Given two wires of the same material, one twice the diameter of the other. If a 
25-gm. weight stretches the thinner wire 1 mm., how much will the same weight stretch the 
thicker wire? 


35 









































Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE. 


EXP. 14 —TENSILE STRENGTH 


Purpose. To measure the tensile strength of various materials. 

Apparatus: Wire-breaking machine; annealed iron, copper, and aluminum wires. Nos. 27 and 30; 
micrometer caliper. 

Note. In physical testing laboratories very strong machines are used to find the breaking 
strength of wires, rods, bars, or cables of various kinds. The tensile strength is measured in 
Kgm. per sq. mm., or in lb. per sq. in. Knowing the tensile strength, an engineer can com¬ 
pute the cross-sectional area of any given material which will be required to carry safely a 
given load. Suppose an elevator is to carry a gross load of 3 tons, and a safety factor of 4 
is required. The strength of the cable for such an elevator must be at least 12 tons. In very 
deep mines the weight of the cable itself becomes an important factor. 

The Micrometer Caliper. For measuring very accurately the diameters of wires and rods 

and the thickness of foil, a microm¬ 
eter caliper is used. The caliper 
shown in Fig. 25 has one fixed jaw, 
and the other is threaded so it can 
be closed gradually. In many mi¬ 
crometers the threads are 0.5 mm. 
apart. Then the head of the screw 
makes two complete turns in closing 
the jaws one millimeter. The head 
is divided into 50 divisions. There¬ 
fore the jaws close 0.01 mm. when 
i. The object to be measured is placed 
between the jaws, and the head is 
turned until the jaws are in contact 
with the object. Undue force must 
be avoided as the instrument is easily 
injured. If the instrument you are us¬ 
ing is not provided with a friction head, 
hold the head rather loosely between the 
thumb and finger, and stop twisting 
just as soon as you feel that contact 
has been made. The divisions on the 
frame read millimeters; those on the 
head read hundredths of millimeters. 
Method. V7ind one end of the wire around the post P and clamp it firmly. See Fig. 26. 

37 




Fig. 26 

















Put the other end through the opening in the shaft S and wind two or three turns on the 
shaft in such a way that the turns of wire hold the end firmly. Set the pawl so the 
ratchet wheel W can turn in one direction only. Then turn the crank slowly until the 
wire breaks, letting the triangular block of wood slip into the slot to hold the spring balance 
at its maximum value. Do not push down on the block. Read the balance and record the 
breaking strength. Two trials should be taken with each sample of wire. With the microm¬ 
eter measure carefully the diameter of each wire. To find the cross-sectional area of the wire, 
square its diameter and multiply by 0.7854 (f tt), or multiply the square of its radius by tt. 
The tensile strength is found by dividing the breaking strength in Kgm. by the cross-sectional 
area. Record only the averages of the separate trials. 

Data. 


Kind of Wire 

Gauge No. 

Diameter 

Cross-sectional 

area 

Breaking 

strength 

Tensile 

strength 












* 


























Calculations: 


Questions and problems. 1. Why 


2. Give three or four cases where 
essential. 


are mine cables sometimes made tapering? 


a knowledge of the tensile strength of materials is 


3. Ask the instructor for the weight of one meter of the No. 27 iron wire. Compute the 
length of such wire that would be needed to break of its own weight, if suspended vertically 
from one end. 


38 















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 
DATE , 


EXP. 15 — CONCURRENT FORCES 


Purpose. (a) To find the resultant of two forces acting at an angle. 

(6) To show that a third force which produces equilibrium with two forces 
is equal and opposite to their resultant. 

Apparatus: Three spring balances, 2000 gm, capacity; wooden block; strong twine; small iron ring, 
I in. diameter; ruler; compasses; three iron clamps, or a board like that shown in 
Fig. 27. (A pastry board, 18x24 in., or a drawing board is cheaper and more convenient 
than the clamps. Several holes may be bored in the board and pieces of J in. dowel 
rod slipped through the rings of the balances to hold them in position.) 


• • • • 
• • • • 


• • • • 
• • • • 
• • • • 
• • • • 


• • • • 
• • • • 
• • • • 
• • • • 


Fig. 27 


Fig. 28 



Note. A man rowing a boat across a stream is carried down-stream by the current. 
Two boys kick a football; one kicks northerly, and the other westerly. The ball moves 
northwesterly. Very often two forces act upon a body at the same point. The angle between 
the forces may have any value from zero to 180°. The resultant of two or more forces is 
that single force which could be substituted for them without altering the effect. When the 
forces act at an angle, the resultant is equal to the diagonal of a parallelogram of which the 
two forces are sides. The equilibrant is a single force which produces equilibrium with two 
or more forces. 


39 


/ 












Method. Cut three pieces of twine about 10 inches long. Fasten one end of each piece 
to the small iron ring. In the other end make a loop to slip over the hook of the balance. 
See Fig. 28. Fasten the balances to clamps along the edges of the table so the tension on 
all the balances will be approximately the same. They should not vary more than 200 or 
300 gm., and no balance should read less than 1000 gm. Adjust the cords on the ring so the 
pull of each balance is in direct line with the center of the ring. 

Place a blank sheet of paper on the board or table so its center will be directly beneath 
the center of the ring. It is a good plan to stick a couple of pins in opposite corners of the 
paper to keep it from slipping while the experiment is being performed. Place a wooden 
block on the paper so that its edge just touches one of the strings, but does not displace it. 
Using a fine-pointed pencil, draw a line along the edge of the block, just under the string. In 
the same manner, mark the direction of the other strings. Read each balance, and record 
its magnitude at the end of the line which represents the direction of the force. 

Remove the paper and produce the lines until they meet. If the work was carefully 
done, the lines will all meet at the same point. Consider this the point of application of the 
three forces. The lines drawn show the direction of the forces, and the balance readings their 
magnitude. 

Select a convenient unit (1 cm. to represent 200 or 250 gm.), and measure off on each 
line the distance needed to represent the balance reading. Using any two of the forces thus 
represented graphically as sides, construct a parallelogram. Draw its diagonal and find its 
magnitude in terms of the scale used. How does it compare with the third force in magni¬ 
tude and direction? 

If the instructor so directs, complete parallelograms with the other forces as sides, and 
draw their diagonals. It is a good plan to represent the forces by solid lines, and use dotted 
lines for the construction lines. 

Problems. 1. What are the chief sources of error in this experiment? 


2. Represent graphically a force of 
30 lb. acting easterly upon a given point, 
and a force of 50 lb. acting southerly. 
Compute the resultant and show the equili- 
brant. (Let ^ in. represent 10 lb.) 


40 


Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 16 — RESOLUTION OF FORCES 


Purpose. To show how a force may be resolved into its components. 

Apparatus; Simple crane boom; two spring balances, 2000 gm.; weights; hanger; screw hooks; 

strong twine; screw eye, or small nail. If the usual form of apparatus is not available, 
a stick 30 or 40 cm. long and about 1 sq. cm. in cross-section may be used for the 
boom. Put the screw eye or a small nail in one end. 




Note. Quite frequently a force acts upon an object in a direction in which the object 
is not free to move. A boy pushes a lawn mower. The direction of the force is at an angle, 
but the mower can not move in the direction of the thrust. The force is resolved into twm 
components, one acting horizontally which moves the mower along the ground, and the other 
acting vertically, which tends to shove the mower into the ground. In Fig. 29, three forces 
act upon the point P. The weight W pulls directly downward, or toward the center of the 
earth. The force measured by the spring balance S pulls along the line PS. A third force 
acts along the line PR, and tends to compress the boom. Of course a crane boom must be 
stiff enough to withstand such compression. In this experiment we shall represent these 
forces graphically and find their magnitude. 

Method. Put the ring of the balance on a hook which may be screwed into the 
upright of the laboratory table. Tack a thin strip of wood to the same upright, about 12 
or 15 in. below the hook. Tie a cord about 2 ft. long to the hook of balance S. Put one 

41 

































end of the stick against the upright, run the cord through the screw eye, or wrap it around 
the nail at the other end, and fasten the weight hanger at the other end of the cord, as shown 
in Fig, 29. Add enough weights to the hanger to make the balance read 1000 or more grams, 
and then adjust the boom so it will be at right angles to the upright. It may be necessary 
to wrap the cord once around the screw eye to prevent slipping. 

Hold a sheet of paper (from back of manual) against the apparatus so the center of the 
sheet will be opposite the point P. Mark the position of P and indicate the direction of the 
thi-ee forces, PW, PR, and PS. How many points are needed to locate a line? 

Read the spring balance S and determine the value of the weights and hanger at W. 
On your paper draw lines to represent the forces PW, PS, and PR. Two of these forces, 
PW and PS are known. Choose a convenient unit to represent them graphically. Draw 
the line PD equal and opposite to PW. Next draw the line PB directly opposite to PR. 
Complete the parallelogram SDBP. (You have given the diagonal PD, the side PS, and 
the included angle.) Find the magnitude of PB from your diagram. Record all values along 
the lines representing the forces. 

To check the value of PB as found by your experiment, hook a spring balance in the 
screw eye at P, and pull in the direction PB just hard enough to pull the boom away from 
the upright. The balance reading should practically equal the value of PB as determined 
graphically. 

If time permits, repeat the experiment, first setting the boom at a different angle, as 
in Fig. 30. The diagram may be made on the other side of the same sheet of paper. 

Question. 1. Name several cases where a force acting in one direction is resolved into 
two components. 


Laboratory Exercises in Physics 
Charles E. Doll 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 17 —PARALLEL FORCES 


Purpose. (a) To show that the equihbrant of two parallel forces is equal to their sum. 

(6) To show that the equilibrant of two parallel forces must be between the 
two, at the center of moments. 

(c) To show that the forces are inversely proportional to the length of the arm 
upon which they act. 

Apparatus: Meter stick; two spring balances, 2000 gm.; three meter stick clamps; weight hanger; 
slotted weights. 



Fig. 31 


Note. Two boys carrying a load on a stick between them furnish an example of parallel 
forces. In Fig. 31 the balance readings represent the forces that the boys exert, and the 
weight W is the load. Two horses pulling a wagon exert parallel forces. A painter’s ladder 
used as a scaffold is supported by ropes that are practically parallel. The stress on these 
ropes varies as the painter walks back and forth along the scaffold. The abutments at the 
end of a bridge represent parallel forces supporting the bridge and its load. As a loaded 
motor truck moves over the bridge, the stress upon the abutments varies. To study such 
cases of parallel forces is the purpose of this experiment. 

Method. Drive two nails in the cross-bar of the table just 80 cm. apart, and place the 
ring of a spring balance over each nail. Put the small clamps on the meter stick, fasten 
one at the 10 cm. mark and the other at the 90 cm. mark. When the clamps are placed 
on the meter stick in this manner, the balances will hang parallel. The third clamp C 
must be between the other two clamps. 


43 


















Fasten clamp C at the 50 cm. mark and read both balances. Call these readings the 
zero readings. Hook the hanger to clamp C, and add afleast 1000 gm. (Include the weight 
of the hanger to find total weight.) Again read the balances A and B. The difference be¬ 
tween these readings and the zero readings gives the true reading for each balance. In this 
manner the error due to the weight of meter stick and small clamps is elhninated. Record 
all readings, the total weight W, and the position of each clamp. Find the sum of the true 
balance readings. Record as error the difference between this sum and the total weight IF. 

The product of the distance AC by the true reading of balance A equals the moment 
tending to produce clockwise rotation about C, if we consider C a fixed point at the center 
of moments. The product of the true balance reading B and the distance CR is the counter¬ 
clockwise moment. The difference between the two moments is to be recorded in the column 
headed “moment error.” 

Move the clamp C to a new position (the 60 cm. mark for example), take all the readings 
as before, and make the calculations. In this case the balances will not be quite parallel, 
since the meter stick is not horizontal. One of the balances may be lowered enough by 
means of a piece of twine to make the stick horizontal. 

The clamp should be moved to a new position for a third trial. 


Data. 


Trial 

BALANCE A 

BALANCE B 

Zero reading 

Final reading 

True reading 

Zero 

reading 

Final 

reading 

True 

reading 

1 







2 







3 








Data (concluded) 


Sum 

Weight 

Error 

Distance AC 

Distance BC 

ClocKwise 

moment 

Counterclock¬ 
wise moment 

Moment 

error 


























Calculations: 


44 

























Conclusions: 


Problem. 1. A bridge is 500 ft. long. It weighs 2000 tons. A locomotive weighing 
500 tons stands 100 ft. from one end of the bridge. Find the strain on each abutment due 
to (a) the weight of the bridge; (6) the weight of the locomotive. 


45 



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I ■ ' ■ 



►V-w V 


1 . 






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1 


. » 


ia 


. -'It 



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k 


• C'. ->• 





t 


9 









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L 




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I 




Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME- 
DATE - 


EXP. 18 —THE PENDULUM 


Purpose. To study the laws of the pendulum and to find the value of the acceleration 
due to gravity. 

Apparatus: Simple pendulum; pendulum clamp; metronome; meter stick; strong thread. A stop 
watch is better than the metronome. A seconds pendulum connected in series with a 
cell and a telegraph sounder makes an excellent time-keeper. 

Note. The chief use of the pendulum is as a time-keeper. As a pendulum swings from 
A to B, Fig. 32, it makes a single vibration. A complete vibration is made by a pendulum 

swinging from A to B and returning to A agair. The num¬ 
ber of complete vibrations a pendulum makes per second is 
its frequency. The period of a pendulum is the time required 
for a complete vibration. The arc AC, or the angle ASC, is 
the amplitude of the pendulum. The length of a simple pen¬ 
dulum is measured from the point of suspension S to the 
center of gravity C of the pendulum bob. 

Suggestion. Two students may work together, one counting sec¬ 
onds as the other counts vibrations. Less confusion is caused if all 
the pendulums are started at the same time, the instructor counting 
seconds as the students count the number of vibrations. 

Method, (a) Fasten one end of a strong thread a little 
more than a meter long to the pendulum bob. Clamp the 
other end securely, taking care that it is exactly 100 cm. 
long. Measure from the point of suspension to the center of 
the bob. Pull the bob to one side a little more than 5 cm., 
and release it. The chord of the arc through which the 
pendulum swings is about 10 cm. While the instructor counts 60 seconds, count the number 
of single vibrations the pendulum makes during that time. 

Suppose the instructor says ‘‘zero” just as the metronome clicks. Both instructor and 
pupil count silently, calling the next vibration “one,” etc. When the metronome has ticked 
60 seconds, the instructor says “sixty,” and the student stops counting with the last vibra¬ 
tion. 

Repeat the experiment. If the results are in close agreement, record and find the average. 
If there is a variation of more than a single vibration, take a third trial, and use the two 
results which are in closest agreement. 



47 













f (5) Repeat the experiment, but pull the bob to one side a little more than 15 cm. before 
starting, to make it swing through an arc of about 30 cm. Count the vibrations just as you 
did in (a). 

(c) Shorten the pendulum to 25 cm., and take two more trials, using a small amplitude. 
If the instructor so directs part of the pupils may use pendulums of 36 cm., 49 cm., 64 cm., 
or 81 cm. 


(d) The following computations are needed: Extract the square root of the length; 
compute the time required for a single vibration in each case. (Carry three decimal places.) 
Rind the value of g from the formula. 


t = TT 



ttH 

or = —. 


Use for TT^ the value 9.8696. 


Data. 


Trial 

Amplitude 

Length 

No. of seconds 

No. of single 
vibrations 

1 





2 





Average 





1 





2 





Average 





1 





.2 





Average 






Data. (Computed results.) Use average values found with small arc. 


Length 

-s/ Length 

Time, single vibration 

Value of g 










48 
























Calculations: 


Conclusions: Answer the following questions in drawing your conclusions. 1. What 
is the effect of amplitude upon the time of vibration? 


2. How does the length of a pendulum affect its vibration rate? What relation exists 
between the times of vibration, t and t', and the square roots of the lengths, \/i and \/J>? 


3. Considering the formula, = —, would you expect a pendulum to vibrate faster 

g 

at the North Pole or at the Equator? 


49 


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Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME, 

DATE. 


EXP. 19 —COEFFICIENT OF FRICTION 


Purpose. To find the coefficient of sliding friction, and to compare sliding friction with 
rolling friction. 


Apparatus: Inclined plane; car; wooden block; clamp; 

meter stick. The plane may be a smooth 
board 6 in. wide and 4 ft. long. 




Fig. 34 


Note. When a block rests upon an inclined plane as shown in Fig. 33, the force of 
gravity acting upon the block is resolved into two components. One component, ED of 
Fig. 34, acting parallel to the plane tends to slide the block down the plane. The other 
component, DF, acts against the plane tending to break it. The ratio of the force ED to 
the force DF is the coefficient of friction for an object on an inclined plane. The coefficient 
of friction may also be defined as the ratio of the force required to slide or roll an object over 
a horizontal surface to the weight of the object itself. 

Suppose we find by experiment that a force of 140 gm. is required to slide a 350-gm. 
block over a horizontal surface. The coefficient of friction equals 140/350, or 0.4. The 
coefficient of friction depends upon the materials- and the nature of the surface. It is lowered 
decidedly by polishing the surface. 

Method, (a) The inclined plane should be placed in the position shown in Fig. 33. The 
slope should be gentle enough so the wooden block, when placed upon the plane, will not 
slide down the plane. Now increase the pitch gradually until a grade is reached at which the 
block will continue to slide slowly down the plane with uniform speed when it is pushed 
gently to overcome its inertia. At this position the grade is just steep enough to exceed the 
angle of repose. 

Measure off along the table exactly one meter from the point where the end of the plane 
touches the table. Find the vertical height of the lower edge of the plane from the table 

51 














at the meter mark. The quotient of the height divided by the base (one meter) equals the 
coefficient of friction. 

In Fig. 34 the triangles ABC and DGF are similar. Therefore, GF: DF =BC:AC. 
But GF equals ED, which represents the force required to slide the block on the plane; DF 
represents the component acting against the plane; BC, the height of the plane; and AC, the 

length of the plane. Whence (coef. of friction) = (height) ^ 

DF AC (length) 

(6) Repeat the experiment, using the car to find the coefficient of rolling friction. In 
this case the plane should be laid flat on the table. One end may be raised by putting a 
lead pencil under it and gradually increasing the pitch until the car will continue to roll 
slowly down the plane, when pushed gently to start it. Measure the base and the height 
as before. 

(c) Repeat (6), but lock the wheels of the car so they will slide. A cut-nail, or wedge- 
shaped block of wood, shoved between the wheels and the frame will serve as an excellent 
brake. 

Data. 


Trial 

Materials used 

Base 

Height 

Coefficient 
of friction 

1 





2 





3 






Calculations: 


Questions and problems. 1. What do you conclude concerning the relative coefficients 
of rolling and sliding friction? 


2. If roads are rough, should carriage wheels have large or small diameters? Use a 
diagram to explain. Can you show by a sketch how rolling friction might be greater than 
sliding friction? 

3. If the coefficient of friction between the 
runners of a sled and snow is 0.1, what force is 
needed to pull a sled of 200 lb. gross weight: (a) 
when the pull is horizontal; (b) when the pull is 
at an angle of 30° with the horizontal? 


52 












Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 
DATE . 


EXP. 20 —THE LEVER 


Purpose. To study the three classes of levers. 

Apparatus: Lever; clamp; scale pans; weights; spring balances, 250 gm. capacity. 



Note. The lever is one of the simplest types of machine. Known as early as the time 
of Archimedes, it was one of the first machines to be used. To-day we find the lever used 
in such devices as shears, can openers, nut-crackers, tongs, pump handles, brooms, shovels, 
etc. The mechanical advantage of any lever equals the length of the effort arm divided by 
the length of the resistance arm. When the lever is in equilibrium, the clockwise and counter¬ 
clockwise moments are equal. When the effort arm exceeds the resistance arm in length, 
the lever is used to multiply force. When the resistance arm is longer than the effort arm, 
the lever is used to gain speed. 

Method. First class. Arrange the lever as shown in Fig. 35 and clamp it firmly. Weigh 
the scale pan, unless its weight is known. Put a 200-gm. weight on the pan marked R 
and place the pan a few cm. (possibly 8 cm.) from the fulcrum. In recording the resistance 
R, the weight of the scale pan must be included. The distance of the resistance from the 
fulcrum is to be recorded as D^. With a weight of 150 gm. in the other scale pan, slide it 
along the lever until equilibrium is secured. The effort is to be recorded in column E, and 
its distance from the fulcrum under Dg. Compute the moments of both the effort and re¬ 
sistance, and find their difference. Find the mechanical advantage by dividing R by E, and 
also by dividing Dg by D,.. Carry two decimal places, and find the difference. 

Repeat the experiment, using different weights in different positions. 

Second class. Put a 200-gm. weight in pan R of Fig. 36, and place it 5 cm. from the 
fulcrum. Hook the spring balance at E, 12 cm. from the fulcrum, and pull it up until 
equilibrium is secured. Record E, R (weight plus pan), Dg, and D,., and make all com¬ 
putations just as you did with the first class lever. In repeating the experiment, use different 
weights and vary the distances. 


53 




























Third class. Place the scale pan with a 50-gm. weight in it, 12 cm. from the fulcrum. 
Hook the spring balance at E, 6 cm. from the fulcrum, and pull up until the lever is horizon¬ 
tal. See Fig. 37. Record all data, and make computations just as you did with the first 
class lever. Another trial, using different weights at different positions, should be taken. 


Data. 


Class 

Trial 

E 

R 

De 

Dr 

E xDg 

R X 

Differ¬ 

ence 

r/e 


Differ¬ 

ence 

First 

1 











2 











Second 

3 











4 











Third 

5 











6 












Calculations: 


Conclusions: The mechanical advantage of any lever may be found 


When-a lever is in equilibrium, the 


Questions. 1. Why must the mechanical advantage of the second class lever always 
be more than unity? 


2. Why must the mechanical advantage of the third class lever always be less than 
unity? 


3. What can you say of the mechanical advantage of a first class lever? 


54 
























Laboratory Exercises in Physics NAME 

Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 

DATE_ 

EXP. 21 —WEIGHT OF LEVER 


Purpose. To show that a lever behaves as if all its weight were concentrated at its center 
of gravity. 

Apparatus: Meter stick; clamp; triangular block; set of weights; spring balance, 2000 gm. 



Fig. 38 Fig. 39 


Note. The center of gravity of an object may be found by balancing it on the edge 
of a triangular block. The center of gravity is directly above the edge of the block. If the 
meter stick used as a lever is supported at any point other than the center of gravity, the 
entire weight of the lever, acting at the center of gravity, tends to produce rotation. When 
we open a door by pushing near the edge, we use the door as a second class lever. If we 
push near the hinge, the door becomes a third class lever. Remember that the resistance 
is concentrated at the center of gravity of the door. Try opening a door (a swinging door 
if convenient) by pushing first near the edge, and then near the hinge. 

Method. Attach the clamp near the zero end of the meter stick and find the combined 
weight of clamp and stick. Locate the center of gravity of the combination by finding the 
position at which it will balance on a triangular block. See Fig. 38. Make a note of the 
position. Next place a 200-gm. weight near the other end of the stick, at about the 95 cm. 
mark, and again balance the weighted stick on the triangular block, as shown in Fig. 39. 
The combined weight of the clamp and stick (concentrated at C) acts upon the arm CF to 
produce a counter-clockwise moment about F. Find the magnitude of this moment. The 
200-gm. weight, acting upon the arm RF, tends to produce a clockwise moment about F. 
Compute its magnitude. 

Repeat the experiment, using a 500-gm. weight at the 90-centimeter division of the 
meter stick. 


55 
























Data. 


Position 
of C. of G. 

Position 

of fulcrum 

Position 
of weight 

Distance 

RF 

Distance 

CF 

Wt. of the 
combination 

Clockwise 

moment 

Counter 

Clockwise 

moment 

Difference 





























Calculations: 


Conclusion: 


It 


Questions and problems. 1. A lever 24 ft. long has a weight of 400 lb. hung at one end. 
balances on a fulcrum placed 4 ft. from the weight. What is the weight of the lever? 


2. From a consideration of this experiment, tell how you could find the weight of a 
lever, having given a clamp, triangular block, and a 1000-gm. weight. 


56 















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 22 —THE PULLEY 


Purpose. (a) To study the mechanical advantage of the fixed and the movable pulley 
and of pulley systems. 

(6) To find the efficiency of the pulley. 

Apparatus: Two single pulleys; two pulleys with two sheaves each; meter stick; spring balance 
250 gm.; set of weights; strong twine. 

Note. The single fixed pulley is used for raising flags, awnings, windows, and other light 
objects. A combination of fixed and movable pulleys is used in the country for putting hay up 
in the mow. In the city, a system of pulleys (block and tackle) forms part of the mover’s 
equipment; it is used to hoist or lower pianos, safes, and other heavy articles of furniture. 
The painter’s scaffold is raised and lowered by a system of fixed and movable pulleys. 

Method. Single fixed pulley. Arrange the fixed pulley as shown in Fig. 40. A weight of 
300 gm. is placed on the hanger R, and enough weights added to hanger E to pull R up 

very slowly. Record the total weight (300 gm. 
plus weight of hanger) in colmnn R; the total 
weight required to raise the hanger R is re¬ 
corded as E + f. This weight represents the 
effort spent in lifting the weight and in over¬ 
coming friction. Next use just enough weights 
to let R move down slowly. The total weight 
(hanger included) at E is now E — f, or effort 
reduced by friction. The average of jF + / and 
E - f is the actual effort E, since by this 
average we eliminate friction. 

Stand a meter stick vertically between E 
and R. Read the position of both, and then 
pull E down through 20 cm., and see how 
much R has been raised in the meantime. 
Divide the resistance R by the effort E to find 
the mechanical advantage. Carry two decimal 
places. Find the mechanical advantage by 
dividing Dg by Dr, and get the difference be¬ 
tween the two quotients. 



57 















































Single movable 'pulley. Arrange the apparatus as shown in Fig. 41. The resistance 
includes weight of hanger and weight of movable pulley. Use a spring balance to find the 
weight of the pulley and also to find the value oi E + f 
and E - f. The distances Dg and Dr may be found by 
the method used with the fixed pulley. Compute the 
mechanical advantage. 


Suggestion. Considerable time will be saved if the in¬ 
structor performs the remaining parts of the experiment in the 
presence of the class as a group. The result is more satisfac¬ 
tory, and less apparatus is required. 





Combination of pulleys, (a) Weigh the movable 
pulley. Arrange the apparatus as shown in Fig. 42, 
and proceed to find E -\-f, E - f, Dg, and Dr just as 
with the single fixed pulley. The weight on the hanger 
should be about 800 gm. to give the best results. 

(6) The resistance R includes the weight of the 
hanger, movable pulley, and the added weights. Ar¬ 
range the combination so the end of the cord will be 
attached to the fixed block as in Fig. 43. Secure all 
the data just as in the preceding cases. 






Fig. 42 


R 

Fig. 43 


Data. 


Arrange¬ 

ment 

E+f 

E —f 

E 

R 

De 

Dr 

R/E 


Differ¬ 

ence 

Theoreti¬ 
cal M. A. 

Effi¬ 

ciency 


















































Efficiency. Find the useful work done by multiplying R by the total work done 

is found by multiplying {E +f) by Dg. The efficiency equals or. ^ Carry 

total work {E+f)xDe 


58 
























































two places and record the efficiency in per cent. In the case of the movable pulleys, the 
resistance to be used should not include their weight. Why? 

Calculations: 


Questions. 1. What is gained by the use of the single fixed pulley? 

2. In one combination, the cord was fastened to the fixed block, and in the other com¬ 
bination to the movable block. How was the mechanical advantage affected? 


3. Diagram a system of pulleys having a mechanical advantage of three. 


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I 


4 


* t 










Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 23 —THE INCLINED PLANE 


Purpose. To determine the mechanical advantage of the inclined plane. 

Apparatus: Inclined plane apparatus; (a board 6 in. wide and 4 ft. long may be used); clamp; 
car, or roller; weights; spring balance, 2000 gm.; meter stick; strong twine. 



Note. The gang-plank to a boat, and a plank used to load heavy objects on a truck 
or wagon, are common examples of the inclined plane. An ordinary road up a hill is an 
inclined plane. The Egyptians are supposed to have used the inclined plane in building 
the great pyramids. Generally the effort is applied parallel to the plane and travels the 
whole length of the plane. It is the purpose of this experiment to learn what fractional 
part of the resistance must be used to keep the load moving when the length and height of 
the plane are known. 

Method. Support the plane as shown in Fig. 44, Weigh the car and add to it a 500-gm, 
weight, calling the total resistance R. By the use of the spring balance the force required 
to pull the car and weight slowly up the plane may be found. This force is to be recorded 
as E + f, or effort plus friction. A second reading taken as the car moves slowly down the 
plane is recorded as E — f, or effort reduced by friction. The average of E + / and E — f 
is the true effort E. 

With a meter stick measure off along the lower edge of the plane just 100 cm. from the 
point of contact with the table, and mark the distance on the edge of the plane. Then 
measure the vertical height of the plane at the 100 cm. mark. If a regular inclined plane 
apparatus is used, the length and height may be read directly from the scales along the 
edges of the apparatus. 

Find the mechanical advantage by dividing the length of the plane by its height. The 
mechanical advantage may also be found by dividing the resistance by the effort. Carry to 
two decimal places and find the difference. 


61 














Two more trials should be taken, using the same method as before, but changing the 
angle of the plane for each trial. 


Data. 


Trial 

E + f 

E — f 

E 

R 

Length 

Height 

R/E 

L/H 

Difference 

1 










2 










3 











‘Calculations: 


Conclusions: 

Problems. 1. What force is needed to move a 1000-lb. wagon up a 4% grade (rising 
4 ft. in 100 ft. of its length), if the efficiency is 80%? (Length is measured horizontally.) 


2. A plane is 20 ft. long and its height is 5 ft. What is the maximum load that a boy 
who exerts a force of 125 lb. can roll up the plane? 


62 
















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 24 — THERMOMETRY 


Purpose. To test the fixed points of a Centigrade thermometer. 

Apparatus: Large funnel, at least 4 in. in diameter; cylinder; boiler, or hypsometer; Centigrade 
thermometer; ring stand and clamp; one-hole rubber stopper, No. 7; snow, or cracked 
ice. 


Note. In graduating a thermometer, the freezing point is determined by packing the 
bulb and lower part of the stem in melting snow or ice. The freezing point of water and the 
melting point of ice have the same temperature. The boiling point is found by suspending 
the thermometer in steam arising from boiling water. If the pressure of the air is 760 mm., 
the boiling point is 100° C. A variation of 27 mm. in pressure causes a variation in the 
boiling point of one Centigrade degree. 





Fig. 45 


Method. Freezing point. Support the thermometer on the ring stand and 
pack the bulb and part of the stem in snow or ice as shown in Fig. 45. 
The snow or ice should reach to the zero mark of the stem. After about 
five minutes, read and record the position of the mercury. Estimate to 
tenths of a degree all thermometer readings. The difference between the read¬ 
ing and the zero point is the freezing point error of the thermometer. If the 
freezing point indicated by your thermometer is too high, the correction is 
marked if the indication is too low, the correction is marked -f. When 
the thermometer is being used, the corrections should be added algebrai¬ 
cally to all readings near the freezing point. 


63 














Boiling point. The thermometer is next put through 
the rubber stopper and suspended in the chimney of the 
boiler as shown in Fig. 46. Enough of the thermometer stem 
should extend above the stopper so a few degrees below the 
boiling point are exposed to view, and the bulb should not be 
nearer the surface of the boiling water than one centimeter. 
The boiling should be continued at least 3 min. after the water 
has begun to boil. Read and record the temperature. 

Water boils at 100° C. under a pressure of 760 mm. Since 
a variation of 27 mm. in the pressure causes a variation of one 
degree in the boiling point, 0.037° must be subtracted from 
100° C. for every millimeter the barometer reads below 760. 
This gives the true boiling point. Read the barometer and 
compute the true boiling point under existing barometric con¬ 
ditions. The difference between the true boiling point as com¬ 
puted and the observed boiling point is the error for the ther¬ 
mometer near the boiling point. This error should be added 
algebraically just the same as the freezing point error. 



Data. 


Freezing 

point 

Observed 

freezing 

point 

Correction 

Boi'ing 

point 

(Computed) 

Observed 

boiling 

point 

Error 

Barom¬ 

eter 









Calculations: 


Curve. Assuming that the bore of the thermometer is uniform, a curve may be plotted 
to show the corrections that must be made at the various points on the scale. On a sheet 
of cross-section paper draw a vertical line 100 spaces long. Mark the top 100 and the bottom 
zero; divide the line into 10 equal intervals to correspond to the 10° divisions on the ther¬ 
mometer. If the freezing point correction was plus, count to the right of the vertical line 
opposite the zero mark one small space for each tenth of a degree correction, and indicate 
this position by a small plus sign. If the correction was negative, count to the left in the 
same manner. Do the same thing with the boiling point correction, and join the two 
points thus found by a straight line. If one correction was plus and the other minus, the 
curve just plotted will cross the vertical line. The correction for any temperature is found 
by counting as tenths of a degree each small space between the curve and the vertical line 
at that temperature. What is the correction at 20° ? What is it at 50° ? 


64 





























Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 25 —EXPANSION OF SOLIDS 


Purpose. To measure the coefficient of expansion of certain metals. 

Apparatus: Coefficient of expansion apparatus; meter stick; thermometer; boiler or hypsometer; 
micrometer caliper; burner; tubes of steel, brass, copper, or aluminum. 

Note. Nearly all substances expand when heated and contract upon cooling. The 
increase per unit length for one degree is called the coefficient of linear expansion. Generally 
such increase is too small to be measured directly; therefore the apparatus used for measuring 
the coefficient of expansion has some device for multiplying the actual increase, so it can be 
more accurately measured. In some cases a rod in a steam jacket expands against the short 
arm of a bent lever, thus forcing the long arm of the lever over a scale. A spherometer is 
sometimes used to measure the expansion directly. The apparatus shown in Fig. 47 gives 
very satisfactory results. 

Method. With a micrometer caliper measure the diameter of the axis A, and place it 
on the rollers so the pointer stands at the zero of the circular protractor. Use a rubber tube 

to connect the end Z? of a brass tube 
to the boiler, and then place the tube 
on the apparatus as shown in the 
figure. See that the groove in the 
tube rests on the edge of the metal 
support. The protractor portion of 
the apparatus should be near the other 
end of the tube. Measure as accu¬ 
rately as possible that portion of the 
length of the tube which lies between 
the two points of support. Take the 
temperature of the room. 

Pass steam through the tube for at least five minutes. As the tube expands, it rolls 
the axis A through a portion of its circumference. Suppose the pointer moves over a space 
of 36 degrees. Then the rod must have expanded an amount equal to 36/360, or 0.1, of the 
circumference of the axis A. If n represents the number of degrees over which the pointer 

moves, and d the diameter of the axis, then -^xvrd = the total increase in the length of 
the rod. 360 

Find the temperature of the steam, and divide the total increase in length by the change 
in temperature of the brass tube (steam temperature minus room temperature) in degrees 
Centigrade. The quotient is the expansion of the entire tube per degree Centigrade. Divide 
this quotient by the length of the tube to find the coefficient of linear expansion. 

65 












In the same manner, find the coefficient of linear expansion of such other metals as the 
instructor may direct. If the Cowen’s apparatus is not available, the method will be some¬ 
what varied and detailed directions may be given by the instructor. 


Data. 


Mate¬ 

rial 

Length in 
mm. 

Diameter 
of axis 

Circumfer¬ 
ence of axis 

Degrees of 
rotation 

Expan¬ 

sion 

Initial temp 
erature 

Final temp¬ 
erature 

Expansion 
per degree 

Coefficient 

expansion 
































Calculations; 


Questions and problems. 
Explain. 


1. One end of a steel bridge is often supported on rollers. 


2. A steel wire is 1000 ft. long at 0° C. Find its length at 60° C. (Coefficient of expan¬ 
sion of steel, 0.000013 per degree Centigrade.) 


66 

















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 26 —EXPANSION OF GASES 


Purpose. To find the coefficient of expansion of gases. 

Apparatus: Tall cylinder, 12 in.; boiler; thermometer; burner; tube and mercury, as described 
below; ice. 

Note. A Frenchman by the name of Charles found that all gases have the same coeffi¬ 
cient of expansion. With gases we do not find the coefficient of linear expansion, but the 
coefficient of cubical expansion, or the increase in volume. A glass tube of uniform bore 
is used for this experiment. The tube should not be more than 1| mm. 
internal diameter and a little more than 350 mm. long. Put a small 
globule of mercury in the tube (not more than enough to make a col¬ 
umn 5 mm. long) and then seal the end so the enclosed air column is 
about 250 mm. long. The tube may be fastened to a section of meter 
stick with rubber bands. See Fig. 48. When the tube is heated the air 
expands and pushes the mercury globule up the tube. The air contracts 
again upon cooling. Of course the density of the air changes, increas¬ 
ing as the air contracts. This change in density is the chief factor in 
convection currents and other atmospheric disturbances. 

Method. Fill the boiler a little more than f full of water, and 
screw on the chimney. The hole at the side of the boiler should be 
closed with a rubber tube and pinch clamp. Light the burner. While 
the water is heating, proceed with (a). 

(а) Stand the tube and scale vertically in the cylinder of ice-water. 
After a few minutes measure the length of the enclosed air column. 
Measure to the lower surface of the mercury globule. Find the tem¬ 
perature of the ice-water, which should be approximately zero. 

(б) Repeat the experiment, using water that has a temperature of 

Fig. 48 about 50° C. In all cases the water should stand at about the same 

level as the globule of mercury. 

(c) For the third trial, the tube should be immersed in steam arising from boiling water. 
The tube and scale may be supported in the chimney of the boiler. Measure the length of 
the air column and read the temperature. Reduce all the thermometer readings to absolute 
temperature by adding 273° to the observed reading on the Centigrade thermometer. 



67 





































Data. 


1, Length of air column at . C., or . A, 

2, Length of air column at . C., or . A, 

3, Length of air column at . C., or . A. 


4. Increase in length between first and second trials . 

5. Increase in length between second and third trials .:. 

6. Total increase in length . 

7. Increase in temperature between first and second trials . 

8. Increase in temperature between second and third trials . 

9. Total increase in temperature . 

10. Amount of expansion per degree . 

Substitute in the following proportion the values you obtained, and divide the product 
of the means by the product of the extremes; original length of air column: final length of 
air column = original absolute temperature: final absolute temperature. The quotient should 
be approximately unity. Why? 


Conclusions: 


Questions: 1. Why is it permissible in this experiment to use the length of the air 
column as the volume of gas? 


2. Why do we always use the absolute temperatures in proportions like that above 
instead of the Centigrade temperatures? 


68 

















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 27 —LAW OF HEAT EXCHANGE 


Purpose. To show that the number of calories lost by a hot substance added to a colder 
one equals the number of calories gained by the latter. 

Apparatus; Calorimeter; thermometer; trip balance; set of weights; ring stand; burner; ice; beaker 
(250 C.C.); wire gauze; magnifier. 

Note. By definition, the weight of a substance in grams multiplied by its change of 
temperature in degrees Centigrade times its specific heat equals calories. When a cup of 
boding water is added to a gallon of cold water, the latter gains as many calories as the 
former loses. The final temperature will be between that of the boiling water and the cold 
water. In all experiments involving heat transfer, the weight of the calorimeter, or container, 
must be obtained, because the calorimeter will have the same temperature as its contents. In 
this manual the student is directed to calculate separately the heat absorbed or lost by the 
calorimeter. If the instructor prefers, the water equivalent of the calorimeter may be obtained 
by multiplying its weight by its specific heat. (Calorimeters are generally made of copper, 
sp. ht. = 0.09.) The product thus obtained may then be considered as so many grams of 
water, and added to the weight of water taken. 

Method. Weigh a calorimeter. Fill it about half full of cold w'ater having a temperature 
of from 6 to 8° C., and weigh again. Have at hand a beaker containing about 150 c.c. of 
water at a temperature of about 60° C. Stir each liquid and record its temperature, estimat¬ 
ing to tenths of a degree. (Use a magnifier.) Then pour the hot w^ater into the cold and 
stir them together quickly until the temperature is constant. Read the thermometer accu¬ 
rately. It is well to have the calorimeter wrapped with asbestos paper or some other heat 
insulator. It should stand on a sheet of such insulator to lessen the conduction of heat to 
the table. Remove the insulating material and again weigh the calorimeter and water. The 
difference between the second and third weighings equals the weight of hot w^ater added. 

Repeat the experiment, using different quantities of water at different temperatures. 


69 






Data. 


1 


2 


Weight of calorimeter . 

Specific heat of calorimeter . 

Weight of calorimeter and cold water . 

Weight of cold water . 

Temperature of cold water and calorimeter 

Temperature of hot water . 

Final temperature of mixture . 

Weight of calorimeter and mixture . 

Weight of hot water . 

Calories gained by calorimeter ... 

Calories gained by the cold water . 

Total calories gained . 

Calories lost by hot water . 

Difference . 

Conclusion: 


Calculations: 


Problems. 1. How many grams of water at 60° C. are needed to raise the temperature 
of a 100-gm. calorimeter, specific heat = 0.09, from 0° C. to 40° C.? 


2. A glass tumbler weighs 200 gm.; its specific heat is 0.2; and its temperature 10° C. 
Find the final temperature if 50 gm. of water at 40° C. are added. (Hint. Let x equal the 
final temperature.) 


70 






























Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 28 —SPECIFIC HEAT 


Purpose. To find the specific heat of some solid. 

Apparatus: Calorimeter; thermometer; boiler; burner; balances; set of weights; piece of twine; 
metal block or shot; magnifier. 

Note. When we find the specific heat of a substance, we determine the number of 
calories needed to raise the temperature of one gram of the substance one degree compared 
to the number of calories required to raise the temperature of one gram of water one degree. 
In the laboratory we generally use the method of mixtures for finding specific heat. By 
PrevosPs theory, we know that when two substances of different temperature are mixed, the 
warmer substance loses heat to the cooler, until both have the same temperature. The total 
number of calories lost by the warmer substance exactly equals the total number of calories 
gained by the cooler substance. 

Caution. In reading the thermometer, be careful to estimate to tenths of a degree. If a small magnifier 
is available, the temperature can be read more accurately. 

If the temperature of the water when starting the experiment is as much below room temperature as 
the temperature of the mixture is above when the experiment is finished, we may assume that the heat gained 
from the room is equal to the heat radiated to it. The calorimeter should stand on a heat insulator. It is 
also well to have it wrapped with asbestos paper during the experiment. 

Be careful to see that no water is carried to the calorimeter with the sohd when it is transferred. 

Method. Tie a piece of strong, light twine to the solid and then 
weigh it. (Students get more satisfactory results when a block of metal 
is used instead of metal shot. A block of aluminum shaped like that of 
Fig. 49 is more satisfactory than lead or copper, since it has a much higher 
specific heat.) Put the solid in a boiler half full of water, letting the 
string hang over the edge so the solid may be easily removed. Light your 
burner. While the water in the boiler is heating, weigh a calorimeter, fill 
it about 2/3 full of water, and weigh again. The water used should be 
about 4° colder than room temperature. Take the temperature of the 
steam arising from the boiling water. (This is also the temperature of the 
solid.) Stir the water in the calorimeter with a thermometer, and take 
its exact temperature just before the solid is to be introduced. By means 
of the cord, lift the solid just above the surface of the water and hold it 
in the steam for a full half minute. Thus the solid is dried thoroughly. 
Then transfer, as quickly as possible, the solid to the calorimeter of cold 
the thermometer, and also agitate the water by lifting the solid up and 
down slowly. WTien the mercury stops rising, read the thermometer. In your calculations, 

71 



water. Stir with 












remember that both the calorimeter and the cold water have gained heat. The metal block 
lost as many calories as the calorimeter and water gained. Since there was no change of 


state, weight in gm. x change in temperature x specific heat = calories. 

Data. 

Weight of calorimeter . gm. 

Specific heat of calorimeter . 

Weight of calorimeter and water . gm. 

Weight of water . gm. 

Weight of metal block . gm. 

Original temperature of water and calorimeter . °C. 

Original temperature of metal . °C. 

Final temperature of water, calorimeter, and metal ... °C. 


Calories gained by calorimeter (wt. x temp, change x sp. ht.) . 

Calories gained by water (wt. x temp, change x 1) . . . 

Total calories gained . 

Total calories lost (same as calories gained) .. 

Calories lost by metal in cooling 1° Centigrade . 

Calories lost by 1 gm. of metal in cooling 1° C. (sp. ht.) . 

Note. It is possible to find the water equivalent of the calorimeter by multiplying the 
weight of the calorimeter by its specific heat. This product may then be added to the weight of 
the water for subsequent calculations, and further calculations pertaining to the calorimeter neg¬ 
lected. 

Calculations: 


Problem. A calorimeter weighing 100 gm. has a sp. ht. of 0.1. It contains 300 gm. 
of water at 20° C. A block of metal weighing 120 gm. and having a temperature of 100°C. 
is dropped into the water. The final temperature is 26° C. Find the sp. ht. of the metal. 


72 
















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 
DATE . 


EXP. 29 —MELTING POINT 


Purpose. To find the melting point of certain crystalline solids. 

Apparatus: Beaker (100 c.c.); ring stand; wire gauze; burner; thermometer, 200° C.; glass tubing, 
4 to 5 mm. diameter; paraffin; solids chosen from the following list: citric acid; tar¬ 
taric acid; benzoic acid; sahcylic acid; cane sugar; naphthalene; stearic acid; resorcin; 
pyrogallol; potassium alum; bismuth; tin; lead. 


Note. The purity of a substance is often tested by determining its melting point; 
Crystalline substances have a very definite melting point, which is the same temperature as 
their freezing point. Noncrystalline substances do not have very sharp melt¬ 
ing points, and the temperature at which they solidify is not always the same 
as that at which they liquefy. 

Method. Unless the students have had experience in glass manipulations, 
the instructor will show them how to draw glass tubing. For this experi¬ 
ment the walls should be very thin, and the internal diameter should be 
reduced until it is about 1 mm. The smaller end is then closed by holding it 
in the flame a moment, and the drawn portion, which should be 5 or 6 cm. 
long, may then be cut off. Two tubes may be made at one time; each 
tube should be slightly tapering. See Fig. 50. 

Fill the beaker nearly full of paraffin and melt the paraffin over a small 
flame. Into one of the tubes introduce enough of the solid selected to fill the 
tube for about 1 cm. of its length. Start with a crystal big enough so it will 
not go quite to the bottom of the tube. By means of rubber bands fasten the 
melting point tube to the stem of the thermometer at such a height that the 
solid will be opposite the bulb. Suspend the thermometer and tube in the 
melted paraffin, and continue to heat the paraffin with a very small flame 
until the solid just begins to melt. Read the thermometer. 

In a similar manner make melting point determinations of such solids as 
the instructor may direct. Do not try to clean the small tube, but throw it 
away and use a new one for each determination. 

Make an alloy by melting together 2 parts of bismuth, 1 part of tin, and 
1 part of lead. Test its melting point in the same way. Suggest some uses to which 
such an alloy could be put. 



Fig. 50 


73 



















Data 


Name of substance 

Melting point 

Melting point, 
from table, 























74 


















Laboratory Exercises in Physics 
Charles E. Dxjll 

Copyright, 1923, by Henry Holt and Company 


NAME_ 

DATE_ 

EXP. 30 —HEAT OF FUSION 


Purpose. To find how many calories of heat are needed to melt one gram of ice. 

Apparatus: Calorimeter; trip balance; set of weights; thermometer; pan for ice; ice; towel. 

Note. We know that it takes only one calorie to raise the temperature of one gram of 
water 1° C. To melt one gram of ice without any temperature change, a large number of 
heat calories are needed. For this reason ice is a very efficient cooling agent. To find just 
how many calories are required to melt one gram of ice, we make use of the method of 
mixtures. The calorimeter and water in this experiment both lose heat. The heat thus lost 
melts the ice, and then warms the ice-water thus formed to the final temperature. 

Method. Weigh the caloruneter; fill it half full of water at about 35° C., and weigh 
again. Break up a couple of hundred grams of ice into lumps about one inch across. Es¬ 
timating to tenths of a degree, read the temperature of the w^ater in the calorimeter. (It 
is better to insulate the calorimeter as directed in Exp. 27.) Add dry ice to the calorimeter, 
a few lumps at a time. Be careful to wipe each piece of ice free from adhering moisture 
before introducing it into the calorimeter, since the chief source of error in this experiment 
arises from the introduction of water with the ice. Stir the w'ater constantly, adding more 
ice from time to time until the temperature is reduced to about 5° C. When the ice is all 
melted, take the temperature. Weigh the calorimeter and contents. The increase in weight 
equals the weight of ice added. 

In exactly the same manner, a second trial should be taken. In calculating your results, 
bear in mind the fact that weight in grams X change in temperature X specific heat equals 
calories, except when there is a change of state. We must also remember that the total 
calories lost by water and calorimeter melted all the ice used (thus forming an equal weight 
of ice-water) and then warmed the ice-water from zero to the final temperature. The differ¬ 
ence between total calories lost and calories needed to warm the ice-water to final tempera¬ 
ture equals the number of calories needed to melt the ice. 


75 






Data. 


Weight of calorimeter . 

Specific heat of calorimeter . 

Weight of calorimeter and water ... 

Weight of water . 

Initial temperature of water and calorimeter . 

Final temperature of water and calorimeter . 

Weight of calorimeter and water, after adding ice . 

Weight of ice used . 

Number of calories lost by calorimeter . 

Number of calories lost by water {cooling to final temperature) . 

Total calories lost . 

Total calories gained {by ice and ice-water) . 

Calories gained by ice water {wt. of ice x Lfinal temperature - zero'] X 1) 

Calories used to melt . gm. of ice . 

Calories used to melt 1 gm. of ice {heat of fusion) . 

Calculations: 


Probleni. An aluminum ball (sp. ht., 0.2) weighs 200 gm. It is heated to 120° C., and 
then laid on a block of ice. The heat furnished by the aluminum is just sufficient to melt 
60 gm. of ice. Find the heat of fusion’ of ice. 


76 


















Laboratory Exercises in Physics NAME 

Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 

DATE 


EXP. 31 —EFFECT OF PRESSURE ON BOILING POINT 


Purpose. To show how a change of pressure affects the boiling point of water. 

Apparatus: Steam boiler, with U-shaped tube containing mercury; burner; thermometer; screw 
clamp; section of meter stick. 

Note. The temperature at which a liquid boils varies with the atmospheric pressure. 

When the pressure is reduced, water boils at a lower temperature than 100° C. Conversely, 

increasing the pressure above 760 mm. of mercury raises the 
boiling point above 100° C. At the top of high mountains, 
the atmospheric pressure is so low that eggs and vegetables can 
not be cooked by boiling. In such places pressure cookers are 
used. The lid of such a cooker fits so tightly that the steam 
can not escape. Hence the steam adds its pressure to that of 
the enclosed air and the boiling point is increased. Water at 
110° C. will cook vegetables tender in about one half the time 
required when the water is only 100° C. 

First method. Fill the boiler nearly half full of water and 
light your burner. The U-shaped piece of glass tubing should 
have at least 5 cm. of mercury in each arm. Adjust the ther¬ 
mometer in the rubber stopper so that the top of the stopper will 
come to the 98° mark, and place it in the chimney of the boiler 
as shown in Fig. 51. The outlet at the side of the boiler should 
be fitted with a rubber tube and screw clamp. Open the tube so 
the water will boil under the pressure of the air only. After 
about 3 min. read the thermometer and the barometer. Close 
the screw clamp so the steam can not escape. One student may 
read the thermometer while another takes the measurements. 
Readings of the thermometer should be taken when the mercury 
Fig. 51 in one arm of the tube stands 10 mm. higher than in the other, 

and again when the difference is 20 mm., 30 mm., and 40 mm. 
respectively. Then open the screw clamp. Calculate what fraction of a degree the boiling 
point is raised by an increase in pressure of 1 mm. of mercury. 



77 

























Data. 


Trial 

Pressure 

Temperature 

Zero 



1 



2 



3 



4 




Total increase in pressure . mm. 

Total increase in temperature .. °C. 

Increase in temperature per mm. increase in pressure . °C. 


Calculations: 


Conclusion: 


Questions. 1. For what purposes are vacuum pans desirable? 


2. What is the advantage of cooking in tightly covered vessels? 


78 















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 
DATE . 


EXP. 32 —EFFECT OF PRESSURE ON BOILING POINT. ALTERNATIVE 


Purpose. (a) To show how a change of pressure affects the boiling point of water. 

(6) To study the advantage of closed vessels for cooking purposes. 

Appar.a.tus: Pressure cooker; thennometer; tripod; burner; potatoes; quart measure; 2-quart 
aluminum pan, or basin. 


Note. See Exp. 31. 



Fig. 52 


Method. (Group experiment.) Put about a quart of water in a 
pressure cooker. See Fig. 52. Clamp the lid on firmly, but leave the 
stop-cock open until the water begins to boil. Read the thermometer 
to find the boiling point at ordinary atmospheric pressure. Then 
close the stop-cock and take successive thermometer readings when the 
pressure gauge shows pressures of 2 lb., 4 lb., 6 lb., 8 lb., and 10 lb. 
respectively. Then calculate the average increase in temperature when 
the pressure is increased 1 lb. per sq. in. A barometer reading of 76 cm. 
is equivalent to 14.7 lb. pressure per sq. in. 


Data. 


Trial 

Pressure 

Temperature 

Zero 



1 



2 



3 



4 



5 




79 



















Total increase in pressure . lb. 

Total increase in temperature . °C. 

Increase in temperature per lb. increase in pressure . °C. 


Method. (Con.) Put a quart of water in an open pan, heat the water to boiling, and 
put two medium-sized potatoes in the pan. Regulate the fire so that the water is kept boiling 
slowly. Note the time when the potatoes are first introduced, and the time when they are 
thoroughly cooked. Time required to cook potatoes, . min. 

Put a pint of water in the pressure cooker and heat it to boiling. Then add a couple 
of potatoes (same size as those used above) to the cooker, clamp the lid in position, and note 
the time. Increase the flame so the pressure will rise quickly to about 20 lb., and then 
regulate the height of the flame so that a pressure of 20 lb. will be maintained for 10 min. 
Turn off the fire and open the stop-cock to let the steam escape. Open the cooker and test 
the potatoes. Are they thoroughly cooked? 

Calculations: 


Conclusion: 


Questions. 1. How does the time required to cook potatoes under 20 lb. steam pressure 
compare with the time required when the water boils at ordinary atmospheric pressure? 


2. How does the temperature of water boiling rapidly in an open vessel compare with 
the temperature of water boiling slowly in the same vessel? Try the experiment. 

3. From your answer to question 2, state clearly how a gas fire should be regulated 
in order to cut the cost of gas bills when boiling vegetables. 


80 






Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 33 —BOILING POINT 


Purpose. (a) To find the boiling point of certain liquids. 

(b) To show the effect of dissolved salts on the boiling point of a liquid. 

(c) To show how mixing liquids affects the boiling point. 

Apparatus: Distilling flask, 250 or 500 c.c.; condenser; 25 c.c. graduate; alcohol, 95%; salt water 
solution, 10%. 

Note. Just as the melting point of a solid may be used to test its purity, so the boiling 
point of a liquid may be used. A pure liquid has a definite boiling point, varying with the 
atmospheric pressure only. When liquids are mixed, the boiling point is generally at some 
temperature between the boiling points of the pure liquids. In general, gases dissolved in 
a liquid lower the boiling point; solids dissolved in a liquid raise the boiling point. 



Method, (a) Set up the apparatus as shown in Fig. 53. Pour 100 c.c. of water into 
the distilling flask and heat it to boiling. Have the bulb of the thermometer about | in. 
from the surface of the water. When the top of the mercury column is stationary, read 
the thermometer. Let the water boil for about three minutes. Does the temperature remain 
practically constant? 

(b) In the same manner, find the boiling point of 95% alcohol. (Use 100 c.c.) When 
you have found the boiling point of the alcohol, remove the flame and pour the distillate 

81 ’ 

















back into the distilling flask. Add 100 c.c. of water, and heat the mixture to boiling. Record 
the temperature. Distil until you have collected 25 c.c. and again read the thermometer. 
Continue the boiling until you have collected three more 25 c.c. portions, reading the ther¬ 
mometer after each portion has been collected. Do not throw away the distillate. It may be 
poured into a bottle designated by the instructor, and used for some other experiment. 

(c) Throw away the liquid remaining in the distilling flask. Rinse out the flask, and add 
100 c.c. of a 10% salt solution. Find its boiling point. Let the solution boil for five minutes. 
How is the boiling point affected as the solution of salt water becomes more concentrated? 


Boiling 'point of water . . . 

Boiling point of alcohol, 95% . 

Boiling point of water and alcohol mixture . 

Boiling point of water and alcohol mixture .(1).; (2) 

(3).; (4). 

Boiling point of salt water, 10% . 

Conclusions: 


Questions. 1. How do solids dissolved in water affect the boiling point? 


2. Do you think that vegetables would cook faster in salt water or in fresh water? 


3. What is meant by “fractional distillation”? 


82 










Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 34 —HEAT OF VAPORIZATION 


Purpose. To find how many calories are required to vaporize one gram of water without 
change of temperature. 

Apparatus; Steam boiler, fitted with rubber tubing, a water trap, and piece of glass tubing 8 in. long; 
calorimeter; trip balance; set of weights; lumps of ice; thermometer. 

Note. It does not take very long to raise a quart of water to the boiling point, but it 
takes more than five times as long to change it all into steam, or vapor. If we test the 
steam from time to time we find that its temperature is constant. All the time that the water 
is “boiling away,” it is absorbing heat. The heat required to vaporize one gram of water- 
(without temperature change) is called the “heat of vaporization.” Since a thermometer does 
not show any evidence of heat absorption, heat of vaporization is often called “latent,” or 
“hidden” heat. That heat is really present may be shown by passing the steam into cold 
water, and noting the rise in temperature. In this experiment, we shall pass a known weight 
of steam into a known weight of water, and then compute the number of calories yielded by 
the steam upon condensation. The heat lost upon condensation equals the heat absorbed 
during vaporization. 

Method. Light the burner under the steam boiler, which should be fitted with a water 
trap as shown in Fig. 54. While the water is heating, weigh the calorimeter, fill it two-thirds full 

of water at about 5° C., and weigh again. Stir the water 
thoroughly with the thermometer, and take its tempera¬ 
ture, estimating to tenths of a degree, just before the steam 
is introduced. Then pass a steady current of steam into 
the water until the temperature rises to about 35° C. 
Remove the glass tube, stir the water thoroughly, and take 
the temperature accurately. Weigh the calorimeter and 
contents; the increase in weight equals the weight of 
steam introduced. The temperature of the steam may 
be read directly from the steam boiler, or preferably, it 
may be computed from the barometer reading. See 
Exp. 24. In the calculations, the student must remember 
that the steam furnished heat upon condensing, and that 
an equal weight of water at 100° C. was formed. The 
water which is thus formed also furnishes heat in cooling 
to the final temperature. 



83 


















Data. 


1. Weight of calorimeter . gm. 

2. Specific heat of calorimeter . 

3. Weight of water and calorimeter . gm. 

4. Weight of water . gm. 

5. Original temperature of water and calorimeter . °C. 

6. Temperature of steam . °C. 

7. Final temperature of water and calorimeter . °C. 


8. Weight of water, calorimeter, and added steam .. 

9. Weight of steam . 

10. Calories gained by calorimeter (wt. x temp, change x sp. ht.) . 

11. Calories gained by water (wt. X temp, change x sp. ht.). . 

12. Total calories gained . 

13. Calories lost by steam in condensing and cooling to final temperature (same 

as cal. gained) .•. 

14. Calories lost by hot water (wt. of steam x [700 - final tempi] x 1) . 

15. Calories lost by . gm. of steam in condensing . 

16. Calories lost by 1 gm. of steam during condensation . 

Calculations: 


Questions and problems. 1. Why does the evaporation of perspiration produce a cooling 
effect? 


2. Can steam be heated above 100° C.? Explain. 


3. How many calories of heat are liberated when 50 gm. of steam condense, cool to zero, 
and freeze to ice at zero? 


84 



















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME, 


DATE 

EXP. 35 —GAS HEATING 


Purpose. (a) To find the cost of heating one quart of water from room temperature to 
the boiling point with a gas burner. 

(6) To test the efficiency of a gas burner under actual working conditions. 

Apparatus; Gas burner, ring or star-shaped type; disc gas meter (American Meter Co., New York, 
N. Y.); 2-qt. tea-kettle; quart measure; thermometer; watch. 

Note. The quality and cost of either gas or coal for fuel purposes are both variable. 
For example, artificial gas may furnish from 450 to 600 B.T.U.’s per cu. ft.; one pound of 
coal may furnish from 10,000 to 15,000 B.T.U.’s. Suppose one is in a locality where gas that 
furnishes 525 B.T.U.’s per cu. ft. is sold at $1.00 per thousand cu. ft., and that coal which 
furnishes 12,500 B.T.U.’s per lb. is sold at $10.00 per ton. For $1.00, a man can buy 
525,000 B.T.U.’s in gas, or 2,500,000 B.T.U.’s in coal. The choice of a fuel must therefore 
depend upon convenience or efficiency. For general heating, gas can not well compete with 

coal. For cooking purposes, gas is a competitor. A gas 
fire is not lighted until needed, and it may be turned off as 
soon as the cooking is finished. The fire is concentrated at 
the point needed. Gas is clean, convenient, and there are 
no waste products to be removed. 

Method. See that the holes at the base of your 
burner are adjusted properly. If the holes are closed too 
much, the flame will burn wuth yellow tips. If they are 
opened too widely, the gas will “roar” and the flame may 
“strike back” and burn at the base. Measure out exactly 
one quart of water from the cold w^ater tap, and pour it 
into a 2-qt. tea-kettle. Connect a piece of rubber tubing 
to the outlet pipe of the dial gas meter. Hold the other 
end of the tubing out the window and let 2 cu. ft. of gas 
escape. Thus the meter is filled with gas and all danger 
from explosion is eliminated. Next connect the meter with 
your burner. See Fig. 55. Take the temperature of the 
water, read the gas meter, turn on the gas and light it 
immediately. Use the full flame of the burner. Just as soon as the water starts to boil, 
turn off the gas. Read the temperature and the meter, and record the time. 

Repeat the experiment in exactly the same manner, but use the flame about two-thirds 

full. 



85 







Data. 


1 


2 


Time at beginning .. . 

Time at end . 

Time required . 

Temperature at the beginning . 

Temperature at end . 

Meter reading, at beginning . 

Meter reading, at end . 

Gas consumed, in cu. ft . 

Cost of gas at current price of . per 1000 cu. ft. 

Conclusion: 


Calculations: 


Method. Part B. Weigh the tea-kettle in lb. Add to it 1| qt. of cold water and weigh 
again. Stir the water thoroughly and take its temperature in Fahrenheit degrees. Read 
the meter, turn on the gas, and light immediately. Just as soon as the water begins to boil, 
turn off the gas, take the temperature of the water and read the gas meter. From figures 
obtained from the gas company find out the number of B.T.U.’s 1000 cu. ft. of gas are 
supposed to furnish, and then calculate the number of B.T.U.’s the amount of gas you used 
to heat the water should supply. In the same manner that you calculated your results in 
Exp. 28, find how many B.T.U.’s were absorbed by the kettle and the water. Bear in mind 
that weight in pounds X change in temperature in degrees Fahrenheit X specific heat equals 
B.T.U.’s. The efficiency equals the total number of B.T.U.’s absorbed divided by the total 
number of B.T.U.’s in the gas consumed. 


86 












Data. 


Weight of tea-kettle . lb. 

Specific heat of tea-kettle . 

Weight of tea-kettle and water . lb. 

Weight of water . lb. 


Initial temperature of water and kettle . 

Final temperature of water and kettle . 

Meter reading, at the beginning . 

Meter reading, at end . 

Amount of gas used . 

Number of B.T.Ui’s absorbed by kettle . 

Number of B.T.U.’s absorbed by water . 

Total number of B.T.U.'s absorbed . 

Number of B.T.U.’s 1 cu. ft. of gas should furnish . 

Number of B.T.U.’s the gas consumed should furnish . 

Number of B.T.U.’s the gas did furnish {Number of B.T.U.’s absorbed) 
Efficiency of burner .. 

Calculations: 


Questions and problems. 1. State as many advantages as you can for the use of gas 
for cooking purposes. 


87 


Pm Pm 


















2, Wluit {\d\‘j\nt{\gi's has coal ovor gas as n fuol for cooking? 


3, If the gi\s has a heat content of 525 B.T.U/s per cu. ft., how much gas would be 
Deeded to heat 3 gallons (24 lb.) of water from 70° F. to 160° F., assuming that the heater 
has an efficiency o^f S0(^? What will be the cost at $1.00 per 1000 cu. ft.? 


Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE_ 


EXP. 36 —RELATIVE HUMIDITY AND DEW POINT 


Purpose. (a) To find the dew point of the air in the room. 

(6) To determine the relative humidity of the air in the room. 

Apparatus: Metal cup, highly polished; thermometer, Fahrenheit; wet-bulb thermometer (the bulb 
of tills thermometer may be surrounded by one end of the wick of an alcohol lamp; 
the other end of the wick should dip into distilled water at room temperature; ice; 
hygrodeik. 

Note. It is well known to all that the air contains water vapor at all times. The 
amount of vapor which the air can hold, or its capacity, varies with the temperature. The 
amount of vapor which the air does hold at a given time is its absolute humidity. The absolute 
humidity depends upon nearness to large bodies of water, upon the temperature, or upon 
winds which carry moisture; the air is not always saturated with moisture. The ratio of the 
absolute humidity to the capacity is called the relative humidity. It tells us the degree, or 
per cent, of saturation. If the air on a warm day is nearly saturated, and a considerable 
cooling occurs, some of the vapor will be precipitated. The temperature at which such pre¬ 
cipitation begins to occur is called the dew point. 

Method. Dew point. Fill the polished metal cup about 1/3 full of water at room tem¬ 
perature. Add a piece of ice and stir with a thermometer. Keep lowering the temperature 
by the gradual addition of ice until a film of moisture appears on the outside of the cup. 
Then read the thermometer at once. Be careful not to breathe against the polished surface. 
Whyf 

Add a little warm water and note the temperature at which the film of moisture disap¬ 
pears. This temperature should not differ from that at which the moisture appeared by more 
than a couple of degrees. The average of the two readings is the dew point. 

Repeat the experiment, using a fresh supply of water and ice. 


Temperature at which moisture appeared... 
Temperature at which moisture disappeared 
Average temperature, or dew point . 


89 









Relative humidity. If a hygrodeik, Fig. 56, is available, two students may be assigned 
to read the thermometers and determine the relative humidity at a certain hour of the day, 

nine o’clock for example. Two other students may take 
the readings an hour later, and so on throughout the day. 
Each reading should be recorded on the blackboard so 
that all the students may get the whole series of readings. 

If a hygrodeik is not avail¬ 
able, the wet-and-dry bulb ther¬ 
mometer may be used. See 
Fig. 57. Read the temperature 
of a dry-bulb thermometer and 
also the temperature as shown 
by the wet-bulb thermometer de¬ 
scribed in the list of apparatus. 

Find the difference between the 
two readings. From Table 58 
in the Appendix the relative 
humidity may be found as fol¬ 
lows: Find the temperature cor¬ 
responding to the reading of the 
dry-bulb thermometer in the left hand column. Read across hori¬ 
zontally from this temperature until you reach the column headed 
by the difference between the readings of the wet-and-dry bulb 
thermometers. The number found at the intersection shows the 
relative humidity in per cent. For example, suppose the dry 
thermometer reads 72° F. and the wet-bulb thermometer only 
64 F. The difference is 8°. Reading horizontally from the num¬ 
ber 72 in the left hand column to the column marked 8°, we find 
the nmnber 65. In this case the relative humidity is 65%. 

Readings may be taken at successive hours as directed for the 
use of the hygrodeik. 



Fig. 56 


Fig. 57 


Data. 


Time 

Humidity 

Time 

Humidity 

Time 

Humidity 

Time 

Humidity 





















• 





90 



























Questions. 1. How is the relative humidity affected by a change of temperature? 


2. Why does a fog generally disappear before noon? 


3. Suppose the dew point is below 32° F. In what form will the vapor be deposited? 


4. Does lowering the temperature affect the absolute humidity? The relative humidity? 


91 




Laboratory Exercises in Physics 
Chables E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 37 — CONVECTION 


Purpose. To show how convection currents are set up in liquids. 

Apparatus: Flask, 50 c.c.; two-holed rubber stopper to fit flask; glass tubing; burner; ring stand or 

tripod; wing top; bottle, with side neck, 1000 c.c.; beaker; rubber tubing; screw 

clamp; metal can, as described below; potassium permanganate solution, |%; battery 

jar, 8 in. or 10 in. 

Note. Convection is one of the most important methods of distributing heat. It 
occurs only in liquids and gases. The general principle of convection depends upon the 
fact that both liquids and gases expand when heated. When such expansion occurs, the 
density is correspondingly diminished. If unequal heating occurs, that portion of the liquid 
or gas which is more highly heated expands and becomes less 
dense. It is then pushed upward by the heavier, colder liquid or 
gas which surrounds it. Thus convection currents are produced. 

Method. Fill the small flask nearly to the top with the 
potassium permanganate solution, and then heat the solution to 
about 60° C. See whether you observe any expansion during 
the heating. Close the flask with the rubber stopper, which 
carries two pieces of glass tubing, one extending almost to the 
bottom of the flask and the other long enough to reach almost 
to the surface of the water in a large battery jar when the 
flask rests on the bottom of the jar as shown in Fig. 58. 

Lower the flask into the battery jar, which should be almost 
full of water. Make a sketch diagram of the apparatus and 
the convection currents which are set up. 



93 

















Fill the metal can (*) shown in Fig. 59 with water. It should then be tightly closed 
with a two-holed rubber stopper. The bottle with the side neck contains a supply of 
cold water. A 500 c.c. filter flask turned upside down may be used if a glass tube is shoved 



Model of Hot Water Tank 


up through the stopper to let in the air. From the opening in the side a glass tube passes 
through one hole of the stopper and extends about two-thirds of the way to the bottom of 
the metal can. The outlet tube B is fitted with a screw clamp S. This tube should pass 
through the stopper, but it must not extend down into the metal can. Place the can on a 
stand or tripod and support the bottle at a higher level. Open the screw clamp and draw off 
enough water into a beaker to make sure that the air is removed from the can. Now heat 
the bent metal tube, using a wing top burner to spread the flame. After two or three minutes 
feel of the metal cup near the bottom and also near the top. 

Results? 

Continue the heating a few minutes longer and then open the screw clamp, catching 
the water which flows out. How does the temperature of the water that flows out compare 
with that in the supply bottle? 


Make a sketch diagram of the apparatus and show by arrows the probable path of the 
water. 


Can may be obtained from Central Scientific Co. 


94 























Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE. 


Exp. 38 —RADIATION AND COOLING 


Purpose. To study radiators and the rate of cooling. 

Apparatus: Bright metal cup; a second cup, same material as first, but coated on the outside with 
lampblack; two thermometers; two beakers, 250 c.c.; one beaker, 1000 c.c.; ring 
stand; ivire gauze; burner; thermos bottle; watch. 

Note. Warm or hot objects radiate heat to the surrounding medium. The rate at 
which heat is radiated depends upon the color of the radiator and upon the nature of its 
surface. How do the outside walls of the cylinders of a motorcycle compare with those of 
the cylinders of the automobile? Explain. Good absorbers of heat, such as 
rough, dark surfaces, are also good radiators. Some substances serve as heat 
insulators. They do not conduct the heat to the surface readily, hence it 
can not be radiated to the surrounding medium. A vacuum is the best heat 
insulator. 


Method. Fill the large beaker with water and heat it to about 80° C. 
With this hot water fill each of the 250-c.c. beakers and transfer it quickly 
to the metal cups, 250 c.c. in each cup. One student should take thermometer 
readings for the polished cup at two-minute intervals while a second student 
takes readings for the blackened cup. Both should continue in this manner 
until 6 or 8 readings have been taken. The temperature of the room should 
also be recorded. 

If a thermos bottle. Fig. 60, is available, the instructor may pour 250 c.c. 
of the hot water into the thermos bottle and let a student take thermometer 
readings at 10-min. intervals thi'oughout the laboratory period. 


Fig. 60 


95 
















Data. 


Time 

Temperature of 
polished cup 

Temperature of 
blackened cup 

Temp, of polished 
cup — room 
temperature 

Temp, of black¬ 
ened cup— 
room temperature 















































Temperature of room.. °F. 

Temperature of water in thermos bottle, 1.; 2.; 3.; 4.; 

5.; 6.; 7.; 8.; 9. 


Conclusion: The rate of cooling is directly proportional 


Questions. 1. Answer the question raised in the introductory note. 


2. From a consideration of your experiment, should steam radiators be highly polished? 
Should they be black? Explain. 


96 




























Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 39 —VELOCITY OF SOUND IN AIR 


Purpose. To determine the velocity of sound in air at room temperature. 

Apparatus: Tuning forks, of known vibration rate (preferably E, 320, and G, 384); glass tube, 1 in. 

to 1^ in. in diameter, and at least 15 in. long; tall cylinder; thermometer; clamp; 
meter stick; flat cork. 

Note. The best resonant length of a closed tube is found to be just one-fourth the wave 
length of the note it reinforces. For example, a tube 1 ft. long produces resonance with a 
sound wave 4 ft. long. If we know how fast a fork is vibrating, we may use a resonant 
tube to find the velocity of sound, since v = nl. Conversely, if the velocity of sound is known, 
it is possible to show that the best resonant length for a closed tube is one-fourth the wave 
length of the note it reinforces. 

Suggestion. When several students in the same room are attempting to find the position of greatest resonance, 
the confusion produced makes it very difficult to get good results. The experiment may be performed by the class 
as a group. 

Method. Fill the cylinder nearly full of water and hold the 
tube in it vertically as shown in Fig. 61. Strike one prong of 
the fork (E) on the piece of cork and then hold it over the end 
of the tube as shown in the figure. Let the wrist remain flexible 
while you are throwing the fork into vibration. Wlrile holding the 
vibrating fork over the tube, move the tube up and down slowly 
until you find a position where the loudest resonance is produced. 
Then clamp the tube in position, and measure the distance from 
the top of the tube to the water level. 

Since the diameter of the tube affects its resonance, the length 
must be corrected for the diameter. The correction is 0.4 the 
inside diameter of the tube. Measure the diameter of the tube, 
multiply the diameter by 0.4, and add the product to the meas¬ 
ured length of the tube. Call the sum V. To find the wave 
length I of the fork we must multiply the corrected length of the 
tube, I', by 4. The student must not confuse length of tube, I', 
with the wave length, 1. V = \l. The wave length multiplied by 
320 equals the velocity. 

Suspend a thermometer in the tube just above the water and find the temperature of 
the air. The accepted value for the velocity of sound in air is found by adding to 332 meters 
(velocity at 0° C.) 0.6 meter for every degree above zero. Call the difference between the 

97 


















measured value and the accepted value the error. Find the per cent, of error by multiplying 
the error by 100 and dividing the product by the accepted value. 

Repeat the experiment, using the G (384) tuning fork. Take all the measurements this 
time in the English system, estimating inches to the nearest tenth. Find the accepted value 
by adding to 1090 ft., 2 ft. for every Centigrade degree above zero. Calculate error and per 
cent, of error. 

Data. 


Length 
of tube 

Diameter 
of tube 

0. 4 X diam¬ 
eter 

Corrected 
length, V 

Wave 
length, 1 

Velocity 

measured 

Velocity 

accepted 

Error 

%of 

error 





























Calculations: 


Questions 
could find the 


and problems. 1. From a consideration of this experiment, tell how you 
vibration rate of a tuning fork. 


2. A closed organ pipe is 8 ft. long. What note does it produce when the temperature 
is 15° Centigrade? 


98 



















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 


DATE __ 

EXP. 40 —VIBRATION RATE OF FORK 


Purpose. To find the vibration rate of a tuning fork. 

Apparatus: Pendulum and tuning fork apparatus, or vibrograph, such as is listed in the catalog of 
any scientific apparatus company; metronome or stop watch; gum camphor or whiting 
and alcohol. 

Note. In this experiment a stylus which is attached to one prong of the tuning fork 
traces a curved path on a smoked glass plate which is drawn beneath it. At the same time 
the pendulum traces a second curve. If we know the vibration rate of the pendulum, it is a 



simple matter to count the number of vibrations the fork makes while the pendulum is making 
one vibration. Then one may calculate the number of vibrations the fork makes in one 
second. See Fig. 62. 

Suggestion. One set of apparatus is sufficient for an entire class, as it takes only a fraction of a second to trace 
the vibrations after the glass is prepared. A little practice is necessary to enable the student to draw the glass at 
the proper speed. There should be a glass plate for two students. A smoked paper may be used, then covered 
with shellac to preserve the record, which may then be mounted in the note-book. 

Method. Prepare a glass plate or paper by covering one side with the smoke from burn¬ 
ing camphor. (The plate may be covered with a coating of whiting and alcohol. As the 
alcohol evaporates the whiting is left as an even coating on the plate.) Lay the plate on the 
apparatus and adjust the tuning fork so the stylus will just touch the glass plate. The stylus 
of the fork should be as close to the pendulum as possible. The pendulum should next be 
adjusted so the point of its needle will just touch the plate as the pendulum vibrates through 
a small arc. Start the pendulum vibrating, and count the number of vibrations it makes in 
one minute. Calculate the time required for the pendulum to make a complete vibration. 

99 









Again start the pendulum vibrating and throw the tuning fork into vibration. This 
may be done by pinching the two prongs together and then releasing them quickly. Draw 
the glass plate beneath the fork and pendulum at such a rate that the pendulum will make at 
least two complete vibrations while the plate is beneath the fork. Count the number of 
vibrations the fork made while the pendulum was making a complete vibration. From the 
time required for the pendulum to make a complete vibration, calculate the number of vibra¬ 
tions the fork would make in one second. 

Data. 

Number of single vibrations pendulum makes per min . 

Number of complete vibrations pendulum makes per min . 

Time required for a complete vibration . 

Number of vibrations fork makes while pendulum makes one complete vibration . 

Number of vibrations fork makes per second . 

Calculations: 


Alternative method. Stretch a No. 26 piano wire across the table and tune it to unison 
with a C tuning fork (256). Measure its length. Then lengthen or shorten the wire until 
it is in unison with the fork of unknown frequency. Measure the length of the wire. Call 
the first length I and the second length V. The frequency of the fork may be found from 
the proportion, 258 : x = I' :l. 

Data. 

Length of string when tuned to unison with C fork .. 

Length of string when tuned to unison with x fork . 

Frequency of fork of unknown vibration rate .. 

Calculations: 


100 










Laboratory Exercises in Physics 
Chahles E. Duel 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 41 —VIBRATING STRINGS 


Purpose. (a) To show how the vibration rate of a string is affected by its length. 

(b) To show how the vibration rate of a string is affected by its tension. 

Apparatus: Tuning forks, C, E, G, and C'; clamp; two triangular blocks; pulley with clamps; hanger; 
set of weights; No. 26 piano wire. 

Note. Every one has seen a violin player tighten the strings of his instrument to 
raise the pitch. As he plays the violin, he changes the length of the strings by placing his 
fingers at different positions. The lengths of strings bear a definite ratio to the frequencies 
of the notes they produce. The vibration rates are also proportional to the forces used to 
stretch the strings. It is the purpose of this experiment to find out what relation exists 
between frequencies and lengths, and between frequencies and tensions. In constructing 
instruments, the manufacturer must study the effect of diameter and density upon the rates 
of vibration. 

Suggestion. Confusion may be avoided by dividing the class into groups for this experiment. Try to have 
in each group at least one student who is musically inclined. 

Method. Lengths. Fasten one end of the piano wire to the edge of the table. Pass 
the wire over the triangular wooden blocks and pulley as shown in the figure. Fasten a 
hanger to the other end of the wire, and add weights to the hanger until the wire is nearly 



in unison with the C tuning fork. See Fig. 63. The wooden block may then be moved until 
the string is in exact unison with the fork. The strings are generally tuned by finding the 
point at which no beats are produced. If a heavy tuning fork is being used, the rider method 
can be used. A paper rider placed on the string will jump off when the string and fork are 
in unison, provided the base of the vibrating fork is held firmly against the table near the 
string. Measure the length of the string included between the triangular blocks. Keeping 
the tension constant, shorten the string by moving the block B until it is in unison with the 
E fork (320). Again measure the length of the string. In the same manner tune the string 

101 












until it is in unison with the G fork (384), and then with a C' fork (512). Record the lengths 
of the strings for each trial. By dividing the frequency of each fork by the frequency of 
fork C (256), we find the simplest ratio of the vibration rates of the forks used. The simplest 
ratio of the lengths of the strings is found by dividing each length by the shortest one. 

Data. 


Vibration rate 

Length of 
string 

Ratio of vibra¬ 
tion rates 

Ratio of lengths 

256 


1.00 


320 


1.25 


384 


1.33 


512 


2.00 



Calculations: 


Conclusion: The vibration rate of a string is 


Method. Tensions. Leaving the block B in the position found for C', read the value 
of the weights and hanger to find the tension of the string. Keep the length constant, but 
take off weights until the string is in unison with G; then read the tension. In the same 
manner remove weights until the string is in unison with the E fork; then remove weights 
again to find the tension needed to produce unison with the fork C. 

Data. 


Vibration rate 

Tension 

Ratio of vibra¬ 
tion rates 

Square root 
of tension 

Ratio of the 
square roots 
of tension 

256 


1.00 



320 


1.25 



384 


1.33 



512 


2.00 




Calculations: 


102 























Conclusion: The vibration rate of a string is 


Problems. 1. A string which is 40 inches long makes 300 vibrations per second. How 
much must the string be shortened to make 400 vibrations per second? 


2. A string which is under a tension of 36 Kgm. makes 384 vibrations per second. What 
will be its vibration rate when the tension is reduced to 25 Kgm.? 




A.. 









■V 









Laboratory Exercises in Physics 
Chables E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 42 —CANDLE POWER 


Purpose. To measure the candle power of several different types of incandescent lamps. 

Apparatus; Meter stick; extension cord, plug, and socket (for two lamps); photometer, any type, 
preferably the Joly photometer described below; lamps of the following type: Mazda, 
clear, 40-watt and 100-watt; Mazda, frosted, 40-watt; Mazda, gas^filled, 150-watt; 
carbon, 16-C.P., about 55 watts. 

Note. The candle power is the unit of intensity of light. Formerly a sperm candle 
was used as the standard for comparing lights, but at present the electric light is generally 
used. If the voltage is constant, the candle power of an electric lamp does not vary to a great 
extent. To compare the candle power of an unknown lamp with that of the standard, a 
screen of some kind is usually placed between the two lamps, and moved back and forth 
until it is equally illuminated on both sides. In the Bunsen photometer a sheet of greased 
paper is used as the screen. When the screen is equally illuminated on both sides, the grease 
spot becomes invisible. In the Joly photometer, two blocks of paraffin are separated by a 
sheet of tin foil. One can easily tell by looking at the edges when the illumination of both 
blocks is equal. With the Rumford photometer, the standard lamp and the unknown lamp 
are adjusted at such distances from a vertical post that the two 
shadows formed by this post on a screen are of equal intensity. 


Suggestion. For use in a room that is to be only moderately dark¬ 
ened, the Joly photometer seems to be easier for students to handle and to 
give the best results. This experiment is very satisfactory as a group experi¬ 
ment. Different members of the class may be assigned to take successive 
readings, but each student should take all the data. If the Rumford or 
Bunsen photometer is to be used, the shght variation in the method may be 
indicated by the instructor. 

Joly photometer. Cut a piece of parawax into two pieces 
and pare the edges down until you have two blocks exactly 2 in. 
square. Lay the broad side on a piece of warm glass until the 
surface melts a little and then place the tin foil on this plane surface and smooth it down 
until it is in close contact. Melt one surface of the other block and put it on the other 
side of the tin foil. This gives us two blocks of paraffin separated by a sheet of tin foil. 
Mount these blocks in a wooden box made as follows: Out of I in. material cut two pieces 
6 in. long and 2| in. wide, and two pieces 6 in. long and 2 in. wide. In the center of one of 
the 2| in. pieces bore a hole 1| in. in diameter. Near each end of one of the 2 in. pieces 
nail a wooden support, grooved so it will slide along a meter stick. See Fig. 64. Nail two 
thin strips to the inside of each 2| in. piece, just far enough apart so the paraffin blocks 

105 





\ 




1 

c 

ca 















when placed at the middle of these pieces will fit snugly between the strips. Then nail 
the four pieces together to make a box, 6 x 2^ x 2|, with the ends open. Drive a small 
darning needle into the lower side of the box, in line with the tin foil, to serve as an indicator. 

Method. Support the meter stick on two grooved blocks and place the photometer 
upon it as shown in Fig. 65. Using a new 25-watt Mazda lamp as a standard, place it at 
the left hand end of the meter stick. Consider its candle power 20, which is nearly correct 
for a voltage of 110. At the other end of the meter stick put the lamp of unknown candle 


D 

Ifll—1 

n 

d' ^ 

rf ^ 1 1 1 M M 1 1 M 

1 in 

1 1 1 1 1 1 IT 


Fig. 65 


power. Use a 40-watt, clear glass Mazda lamp for the unknown lamp. Move the photom¬ 
eter back and forth along the meter stick until a place is found where the edges of the paraf¬ 
fin blocks appear to be equally illuminated. Measure the distance (D) from the standard 
lamp to the screen, and the distance (D') from the lamp of unknown candle power to the 
screen. Square both distances, and divide {D'y by (D)^. The quotient tells you how many 
times as strong the x lamp is as the standard lamp. To find the candle power of the x lamp, 
we multiply the quotient just found by 20, the candle power of the standard. 

In the same manner, find the candle power of such other lamps as the instructor may 
direct. It will be of interest to include for comparision a 100-watt Mazda, a 40-watt Mazda, 
frosted glass, a 150-watt Mazda, gas filled, a carbon filament lamp, 16-C. P., or about 55-watt, 
and a 40-watt Mazda, clear glass, held with the tip of the bulb toward the screen. 


Data. 


Kind of Lamp 

Watts 

Distance 

D 

Distance 

D' 

(D)2 

(D')2 

(DO 2 
(D)2 

Candle 

power 

Watts per 
Candle 










































































106 

























Calculations; 


Questions. 1. From the results of your experiment, explain why carbon filament lamps 
are rapidly becoming obsolete. 


2. What do you understand by the terms maximum candle power? minimum candle 
power? and mean spherical candle power? 


3. How does a frosted bulb affect the candle power? What advantage has it? 


107 


I 





mt ^ 






t 



I 








r. 
















L 



1 - 


J 




Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE 


EXP. 43 — REFLECTION OF LIGHT 


Purpose. (a) To show that the angle of reflection of light is equal to the angle of incidence. 

(6) To show how images are formed by plane mirrors. 

Apparatus: Plane mirror; rectangular wooden block; ruler; protractor; pins. For alternative method, 
piece of plane glass, 2x4 in. 

Suggestion. It is possible to avoid errors due to refraction by using instead of the silvered mirror a 
piece of plate glass which has been blackened on one side by the soot from burning camphor. The soot should 
then be brushed over with shellac and covered by a sheet of black paper before the shellac dries. This gives 
a permanent mirror. The front surface of this mirror should be placed on the mirror hne when used as 
directed below. 

Note. In this experiment, one can easily prove that a ray of light which is reflected 
back from a mirror makes the same angle with the normal to the mirror that the incident 
ray makes. The image of a point in a plane mirror appears to be back of the mirror at some 
point in the reflected ray produced. By locating two reflected rays at different angles and 
then producing them until they meet behind the mirror, we may locate the image of a point. 
In turn, the images of enough points to outline the object may be found in the same manner. 

Method. Draw a line across the middle of a blank sheet of paper. Then draw a scalene 
triangle not nearer the median line than 4 cm. No side of the triangle should be shorter 
than 4 cm. Saw into a wooden block for about \ in., and insert one end of the mirror in the 
saw-cut to hold it vertically or fasten a mirror to the wooden block by means of a pin driven 
into one end of the block and then bent around to hold the mirror vertically, as in Fig. 66. 
Place the block and mirror on the sheet of paper so the back edge of the mirror will just 
coincide with the median line. If the blackened mirror is used, the front edge should be 
placed on this line. Be sure that the mirror stands vertically. 



Fig. 66 


Stick a pin at one of the vertices of the triangle. Lay a straight-edged ruler on the 
paper, at D for example, Fig. 67, so the angle AOD will be practically a right angle. Sight 
along the edge of the ruler at the image of the pin A as seen in the mirror. Use the ruler 
just as if you were shooting along its edge at the image of pin A. Then draw a line along 
the edge of the ruler, using a very sharp-pointed pencil. In the same manner, locate a second 
sight line for pin A from an entirely different angle, as at E. Draw this line and letter both 

109 












sight lines A. Then, without moving the mirror, locate two sight lines for a pin placed at B, 
and two more for a pin placed at C. 

Remove the mirror and produce the two sight lines until they meet behind the mirror 
line. Use dotted hnes beyond the mirror line. Call this point of intersection A'; it is the 
image of A. Join A and A'; measure the distance of each from the mirror line, and record 
the distances on the lines themselves. 

In the same manner produce the sight lines for R until they meet to form the image of 
B at B'. Join B and B', and measure their distances from the mirror line. 



Fig. 67 


Proceed in the same manner with the sight lines of C, producing them until they meet 
at C'. Join C and C', and measure their distances from the mirror line. Connect A' B' C 
with dotted lines. 

From the point where the first sight line for A intersects the mirror line at 0 draw a 
line to A. Erect a perpendicular OP to the mirror line at 0. Using a protractor, measure 
the angle of incidence AOP and the angle of reflection DOP. Record the values of these 
angles at their vertices. 

Questions. 1. How does the triangle A'B'C' compare in size with ABCf 

2. Compare the relative distances of object and image from the mirror. 

3. What angles do the lines AA', BB', and CC' make with the mirror line? 

4. How do the angles AOP and DOP compare in magnitude? 

5. Describe the image of an object as formed by a plane mirror. 


110 









Alternative method. For the benefit of students who have great difficulty with sight 
lines, the following method is given. Draw the mirror line and the triangle just as directed 
in the preceding method. Use a piece of plane glass instead of the mirror. Fasten it to the 
wooden block with a pin in the same manner as directed and place the glass on the mirror 
line. Place a book 6 or 8 in. back of the glass plate to make a dark background. By looking 
through the glass at a slight angle, a faint image of the pin at A may be seen back of the 
glass plate. Reach behind the plate and stick a pin at the exact spot where the image of the 
pin A appears to be. Label this point A'. In the same manner stick a pin at B and locate 
its image at B'. Likewise find the position of the image of C at C'. 

Stick a pin a couple of inches from B at such an angle that it makes a straight line with 
B and the image of A as seen in the glass plate. Remove the glass plate. Draw a line 
through these two positions and produce it to the mirror line. Mark the point of intersection 
0. The line just drawn is the path of a ray of light reflected from the glass plate; the 
incident ray comes from the pin at A. Draw AO, the incident ray, and then erect the per¬ 
pendicular OP to the mirror line at 0. With a protractor measure the angle of incidence 
AOP and the angle of reflection BOP. 

Join A', B', and C' with dotted lines. Connect A with A', B with B', and C with C', 
making the lines dotted beyond the mirror line. 

If the student uses this method, he should answer all the questions that follow the first 
method. 


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Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 44 —INDEX OF REFRACTION 


Purpose. To measure the index of refraction of a ray of light passing from a piece of 
plate glass into air. 

Apparatus: Piece of plate glass, about 3 in. square; ruler; pencil compasses; pins. 

Note. A ray of light passing obliquely from air into glass is bent out of its course, and 
toward the normal drawn to the two surfaces at the point of incidence. As the ray leaves 
the glass, it is bent from the perpendicular. The ratio of the sine of the angle of incidence 
to the sine of the angle of refraction is called the index of refraction. The index of refraction 
varies in different kinds of glass. The addition of lead in the manufacture of glass increases 

the index. Cut glass is denser than ordinary window 
glass, because lead is added to increase the index oi 
refraction and enhance its brilliancy. 

Sine defined. Suppose we have given the right tri~ 
angle ABC of Fig. 68. The sine of the angle BAG is 
defined as the ratio of the length of the side a opposite 
the angle to the hypotenuse c. If the triangle is made 
larger without increasing angle BAC, the ratio is not 
affected. The quotient of a' divided by c' is exactly 
equal to a/c. Tables showing the sines of all angles from 0 to 90° have been prepared. 
Likewise, 6/c, the sine of angle ABC, is exactly equal to h'/c', the sine of angle AB'C\ 



113 










Method. Place the plate of glass on the center of a blank sheet of paper and outline it 
with a sharp-pointed pencil. About f in. from the upper right hand corner of the plate stick 
a pin A as close to the glass as possible. At B, about 1 inch from the lower left hand corner, 

stick a second pin, close to the plate. At C, not less 
than 2 in. from B, stick a third pin in line with B 
and the image of A as seen through the glass. (Do 
not align the pins with A as seen over the glass 
plate.) 

Remove the glass plate. Draw the line AB, 
which represents the path of a ray of light traveling 
through the glass plate. Also draw BC, which 
represents the refracted ray, since AR is bent as it 
leaves the glass. At B construct perpendiculars to 
the line DE as shown in Fig. 69. 

From J5 as a center describe two arcs, one inter¬ 
secting OB and AB; the other intersecting BC and 
BP. Use the same radius for both arcs. 

From the point of intersection of the arc with 
line AB, draw a line y perpendicular to OB, and 
measure this line in millimeters. Write its value just 
above the line itself. 

From the point of intersection of the other arc 
with BC, draw a line x perpendicular to BP, and 
measure the line in millimeters. Record its value. 
The length of the line y divided by the length of the 
line X is the index of refraction from glass into air; the quotient x/y is the index of refrac¬ 
tion from air into glass. 

By means of a protractor measure the angles ABO and CBP, and from the table of 
sines in the Appendix find the sine of each angle. Divide the sine of angle CBP by the sine 
of angle ABO to find the index of refraction from air into glass. 

If the glass plate is square, place it on the paper again and stick a pin at F, the same 
distance from the lower right hand corner that A is from the upper right hand corner. Stick 
a pin S in line with F and A as seen through the glass. Does refraction occur when a ray of 
light passes from glass into air at an angle of 90°? 

Conclusion: The index of refraction of the plate of glass I used is. 

Questions. 1. What practical uses can be made of the index of refraction? 



Fig. 69 


2. The index of refraction of the diamond is approximately 2.5. What is the speed of 
light in the diamond? 


114 












Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 45 —INDEX OF REFRACTION 


Purpose. To find the index of refraction of a ray of light passing from air into water. 

Apparatus: Battery jar, 5 in. in diameter, 6 in. deep; metal sheet, preferably of zinc. The strip should 
be a little more than 5 in. long and 2^ in. wide; it may be cut so that the 2 in. portion 
(see Fig. 70) just fits into the battery jar. Very thin metric ruler, or a strip of zinc 
8 in. long and j in. wide, pointed at one end; pencil compasses. 


— --— —5 inin. 


Fig. 70' 


--- ^ 


Note. We do not see objects in their true position in 
water. To a man on the bank of a stream, a fish appears to 
be higher than it really is. To the fish the man has the same 
appearance. Even when we look vertically into water, the 
water appears to be only three-quarters of its true depth. In 
this experiment we shall attempt 
to find just how much a ray of 




Fig. 71 


light is bent as it passes obliquely from air into water, or 
vice versa. 

Method. Place the metal sheet in the batteiy jar so it 
will stand vertically along the diameter of the jar. Then fill 
the jar with water just to the V-tip of the metal sheet. Fig. 71. 

While looking over the edge of the jar, at right angles to the 

metal sheet, shove the metal strip 
or a thin metric ruler down just 
inside the opposite side of the jar 
until the lower end B (Fig. 72) 

appears to be in line with the edge of the glass A and the metal 
tip V. Then measure the distance CB from the top of the 
jar to the end of the ruler or strip, and the distance NB 
from the end of the ruler to the water surface. Also meas¬ 
ure the distances AM, AS, and SC. 

In the space on the opposite side of this sheet of paper 
draw a horizontal line, MN, about 1/3 of the way down, to 
represent the water surface. At the center oi M N erect a 
perpendicular to represent the metal sheet S V . Make all 
drawings to scale, just one-half the size obtained by measure¬ 
ment. Draw VS, AS, and SC to scale, making the line AC 
parallel to the line MN, since AM and CN will be approximately equal to F*S if the work was 
well done. From C draw a line downward parallel to VS, producing it beyond N to repre- 

115 


Fig. 72 

































sent the distance NB. Next draw ^ F to represent the incident ray, and VB to represent ^ 
the refracted ray. The line SV should be produced below MN. 

With a pair of compasses measure off on line VB a, distance Vx equal to A V. From 
the point x draw a line xT perpendicular to the line SV produced. 

The length of the line .diS divided by the length of the line xT is the index of refraction 
between air and water. 

If the instructor so directs, the student may measure the angles A VS and BVT with a 
protractor and find the value of their sines from the table in the Appendix. (See definition 
of sine under Exp. 44.) Then the index of refraction is equal to the sine of the angle A F^ 
divided by the sine of the angle BVT. 

Conclusion: The index of refraction of a ray of light passing from air into water is 


116 



Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE_ 


EXP. 46 —INDEX OF REFRACTION 


Purpose. To find the index of refraction of a ray of light passing from air into water. 
(Alternative method.) 

Apparatus: Boards of the shape shown in Fig. 73 form a part of the equipment of some laboratories. 

They can be easily made by the instructor or by some of the boys under his direction. 
A battery jar 8 in. in diameter and 10 in. deep is desirable. Ruler; compasses; pro¬ 
tractor; pins. 



Suggestion. If the board is to be made in the laboratory a stick I 5 in. square and 9 in. long may be 
used as the support. The board itself may be cut from i in. pine of the dimensions indicated in the figure. 

Note. See Exp. 45. 

Method. Fasten a piece of light cardboard or stiff paper to the board with thumb-tacks. 
Stick a pin B about 3 in. below the center of the supporting stick. Near the right hand 
edge and about 3| in. lower down stick a second pin C. Place the board across^ the middle 
of the battery jar and fill the jar with water up to the level of the pin B. To indicate the 
water level stick a pin N just at the surface of the water and near the right hand edge of 
the board. Near the top of the board stick another pin in line with the pin B and the pin 
C as seen through the water. 

Remove the board from the jar and take off the cardboard. Letter each of the pin¬ 
pricks. The cardboard may now be dried between paper towels, laid on a blank sheet of 

117 

















note-book paper, and the position of the sight lines transferred by pricking through the note¬ 
book paper with a pin to locate the position of each of the four pinholes on the cardboard. 

On the blank sheet of note-book paper draw the line 
J5C, which represents the incident ray; and the line AB, 
which represents the refracted ray. From N draw a line 
through B to M to represent the surface of the water. At 
B erect a perpendicular to MN and produce it downward 
to P, similar to Fig. 74. 

With a protractor measure the angles ABO and CBP. 
From the table of natural sines in the Appendix find the 
sines of these angles. The index of refraction from air into 
water equals the sine of angle ABO divided by the sine of 
angle CBP. 

We may also find the index by the following method: 
Draw AO parallel to MN. On BC measure off a distance 
Bx equal to AB, and from x draw a line xy perpendicular 
to BP. The index of refraction equals the length of the line 
AO divided by the length of the line xy. 

Conclusion: The index of refraction of a ray of light passing from air into water is 



118 







Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE_ 


EXP. 47 —STUDY OF LENSES 


Purpose. (a) To find the focal length of a double convex lens. 

(b) To show how images are formed by convex lenses. 

(c) To show the relation between the size of object and image. 

Apparatus: Light box, electric bulb, or gas jet; meter stick; supports; lens holder; screen holder; 
ground glass plate. 

Note. The thicker a lens is in proportion to its diameter, the shorter its focal length. 
If a lens is made of ordinary crown glass, index of refraction about 1.5, its focal length and 
its radius of curvature will be nearly equal. It is possible for a lens to have a different 
radius of curvature for its opposite sides. For that reason it is desirable to have the same 
side of the lens toward the object throughout the experiment. In finding the focal length 
of a double convex lens, we assume that the sun’s rays are parallel. We know that by defini¬ 
tion parallel rays are refracted so that they meet at the principal focus. 

Suggestion. Experience shows that this experiment is quite as satisfactory when the instructor works 
with the class as a group, since the students thus acquire a more thorough understanding of image formation 
than is possible by the usual individual effort. The expense will not prohibit the buying of one good optical 
bench, the Farweli-Stifler for example, which will be found very useful for demonstration work. 



Method. Focal length. Put the lens in a lens holder and place it on the 50 cm. division 
of the meter stick. Place on the meter stick a screen holder which carries a ground-glass 
plate 2 or 3 in. square. See Fig. 75. Point the meter stick toward the sun, and then move 
the screen along the meter stick until the image of the sun that is formed is as nearly as 
possible a point. The distance from the lens to the glass plate is the focal length of the lens. 

If the day is cloudy, open a window, and point the meter stick toward a house or a tree 
several hundred feet distant. The meter stick and lens should be back from the window a 
distance of several feet. Move the screen until a small, distinct image of the house or tree 
is formed upon it. The distance between the lens and the screen is the approximate focal 
length. This method is not quite so accurate as the first one. 

The focal length of lens No. is . cm. 

119 


















Method. Images. Place the gas jet or light box which is to be used as the object at 
one end of the meter stick. Place the lens far enough away from the object so it will be dis¬ 
tant more than twice the focal length of the lens. Move the ground-glass screen ajong the 
meter stick until the image that is formed upon it is the best defined that it is possible to get. 
Read and record the position of the object, the lens, and the screen. Measure also the height 
of the object and the height of the image. Call the height of the object Sg and that of the 
image Si. (Case 2.) 

For the second trial move the lens until it is distant from the object exactly twice the 
focal length. Then adjust the screen until the best defined image is obtained. Read all 
positions and measure the heights of object and image as before. (Case 3.) 

Next have the lens distant from the object more than once and less than twice the 
focal length. Adjust the screen to secure the best image and take all measurements as before. 
(Case 4.) 

Try to throw a distinct image on the screen when the object is distant from the lens 
exactly its focal length (Case 5) and again when the object is nearer the lens than a focal 
length. (Case G.) 

Find the distance Dg of the object from the lens in all cases and the distance Z),- of the 
image. Divide 1 by Dg and carry three decimal places. Proceed in the same manner to 

to find and i. Divide Dg by D;, and Sg by >S,-; carry three places. 

Ui 1 


Data. 


Position 

of object 

Position 

of lens 

Position 

of image 

Object 

distance 

Do 

Image 

distance 

Di 

1 

D o 

JL 

D i 

- + 1 
Do Dj 

1^ 

F 

So 

Si 

Do 

Di 

So 

S i 






















































Calculations: 


120 




















Conclusions: State the relationship you find existing between Dg, Z),-, and F. 

State also the relation existing between the relative sizes of object and image and their 
relative distances from the lens. 


Problem. A stick 4 ft. high is 6 ft. from a lens which has a focal length of 6 in. How 
far away is the image formed? How high is the image? 


121 


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NAME 


Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


DATE 


EXP. 48 — MAGNIFYING POWER 


Purpose. To find the magnifying power of a double convex lens. 

Apparatus: Lens, about 10 cm. focal length; ring stand, with two rings, one of them about 1 in. m 
diameter; piece of cardboard with hole just 1 cm. square cut in the middle; section 
of meter stick. 

Note. In Exp. 47 we found that a real, inverted image can not be formed upon a screen 
if the object is nearer the lens than one focal length. When the object is brought a little 
nearer the lens than one focal length, an enlarged, virtual image is 
produced. While this image can not be thrown upon a screen, it 
may be seen by placing the eye close to the lens, on the opposite side 
from the object. The reading lens, or the simple magnifier, is used 
in this manner. In this experiment, we shall observe with one eye 
an unmagnified scale at the least distance for distinct vision, while 
the other eye sees the scale as magnified by the lens. The least dis¬ 
tance for distinct vision with the normal eye is 25 cm., or 10 in. 



Method. First find the focal length of the lens just as you did 
in Exp. 47. Then place the lens L upon the rim of the small ring 
and fasten the ring on the ring stand at a height of 25 cm. (10 in.) 
above the section of meter stick as it lies on the table. 

Lay the cardboard across the other ring, which should be 
clamped directly beneath the lens, at a distance equal to one focal 
length, or a trifle less than its focal length. See Fig. 76. 

Hold one eye as close as possible to the lens and look through it 
at the hole in the cardboard. With the other eye look past the edge 
of the cardboard, and count the number of millimeters on the 
section of meter stick which appear to be included by the square 
opening. Divide the number of millimeters counted by 10 (the width of the opening) to 
find the magnifying power of the lens. 

The magnifying power of the lens may also be found by dividing the least distance 

, .» . 25 cm. 

for distinct vision by the focal length of the lens. By formula, magnifying power-— , 


or 


10 in. 


123 





















Focal length of lens . cm. 

Width of opening .. cm. 

Apparent width of opening ... cm 

Magnifying power of lens, by experiment . 

Magnifying power of lens, by formula . 

Questions. 1. A linen tester has a focal length of 2 cm. Find its magnifying power. 


2. A reading glass has a focal length of 6 in. What is its magnifying power? 







Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE_ 


EXP. 49 —THE MICROSCOPE AND TELESCOPE 


Purpose. (a) Study of the compound microscope. 

(b) Study of the astronomical telescope. 

Apparatus: Optical bench of some type, including light, and screen; lenses, ranging from 3 cm. to 
6 cm. in diameter, and having focal lengths ranging from 5 to 15 cm. 

Note. In Exp. 48 we learned that a virtual, enlarged image may be seen through a 
double convex lens when the object is a little nearer the lens than the principal focus. In 
the use of a compound microscope, an objective lens system is used to form an enlarged, 
real, inverted image of the object. The object is distant from the lens just a trifle more than 
one focal length. (Case 4.) When the image formed by the objective lens is viewed through 
an eye-piece acting as a simple magnifier, it is magnified again. 

With the astronomical telescope the nearest heavenly body must necessarily be distant 
many times the focal length of the objective. Therefore the objective forms a real, inverted 
image, smaller than the object. Since the objective lens may range from a few inches in 
diameter to a few feet, it collects a large number of light rays. The eye-piece, which is of 
very short focal length, acts as a simple magnifier. 



Method. Find the focal length of both lenses by the method described in Exp. 47. 
Neither lens should have a focal length of more than 10 cm. Assemble the apparatus as 
shown in Fig. 77, The light should be surrounded by an opaque screen, or a cardboard 
cylinder. The opening in the screen, which we may call the object AB to be magnified, 
should not be more than 5 mm. square. Place the objective lens 0 on the meter stick so 
that it will be distant from the opening AB a little more than the focal length of the lens. 

Find a position for the ground-glass screen where the best defined image of the object 
is produced. Then find a position for the eye-piece lens L where it will give as high a 
magnification of the rough surface of the ground-glass screen as possible. 

125 























By placing the eye close to the lens L, an enlarged, inverted image of the aperture can 
be seen when the ground-glass screen is removed. 


Focal length of objective . cm. 

Focal length of eye-piece . cm. 


The Telescope. 



Method. After finding the focal length of both lenses, place the objective lens near one 
end of a meter stick as shown in Fig. 78. The objective lens should be at least 6 cm. in 
diameter and of not less than 15 cm. focal length. The eye-piece should have a focal length 
of 10 cm. or less. (5 cm, is better). Standing about 10 feet from an open window, point 
the meter stick toward a house or a tree a few hundred feet away. Slide the ground-glass 
screen along the meter stick until a position is found where a sharply defined image is pro¬ 
duced. Note the size of the image as compared with the object. 

Place the lens L on the meter stick and move it to a position where it will magnify the 
rough surface of the ground-glass screen as much as possible. Remove the screen and again 
point the meter stick toward the house or tree. When the eye is held close to the eye-piece 


an enlarged, inverted image may be seen. 

Focal length of objective . cm. 

Focal length of eye-piece . cm. 


Questions. 1. In the microscope state clearly the function of the objective. Tell where 
the object is placed with reference to the objective. Tell where the image is formed. 


2. What is the function of the eye-piece in both the microscope and the telescope? 



















3. What is the purpose of the objective in the telescope? Where is the image formed? 


4. If the telescope just studied were to be used for studying terrestrial objects, where 
would an extra lens have to be placed? 


127 






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Laboratory Exercises ia Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 50 —MAGNETS AND MAGNETISM 


Purpose. (a) To learn how to make a magnet. 

(6) To find what materials are attracted by a magnet. 

(c) To show polarity and its effect. 

(d) To learn what materials are transparent to magnetism. 

(e) To study induced magnetism. 

Apparatus: Bar magnets; steel knitting needles, some of them cut in two; large darning needles; 

compass; burner; forceps; iron filings; bits of glass, wood, copper, nickel, zinc, aluminum, 
and tin; wooden support for magnet; sheets (about 4 in. square) of copper, zinc, lead, 
wood, glass, aluminmn, tin, and iron; cut nails; tacks or brads. Old watch springs 
may be obtained from jewelers, and short pieces used instead of the needles. 


Note. In this experiment we desire to learn how to make a magnet and how a magnet 
may be destroyed. Polarity is the sure test for magnetism, since there are other causes for 
attraction besides magnetism. In order to secure good results in the experiment, all iron or 
steel must be removed at least one meter from the magnet that is being tested. A magnet 
temporarily induces magnetism in any piece of iron or steel which happens to be near the 
magnet. 

Making Magnets. Holding a darning needle, stroke the needle with the N-pole of a 
bar magnet, beginning at the eye of the needle and ending at the point. Return to the starting 
point through the air-gap. After 12 or 15 strokes test the needle for magnetism by putting 
it in iron filings. Bring the point of the needle near the N-pole of a compass needle. Result? 

. Hold the eye of the needle near the 

N-pole of the compass needle. Result?. 

In the same manner magnetize a piece of knitting needle. Then hold it with the forceps 
in the flame of a burner until it is heated red hot throughout its length. Let it cool, while 
the ends point in an East and West direction. Test it for magnetism with iron filings and 

with the compass needle. Results? . 

Magnetize a second piece of knitting needle as before and then break it into several pieces. 

What is the effect of breaking a magnet?. 

Conclusions: 


129 










Magnetic Materials. Using a bar magnet, test each of the following bits of material to 
see which ones are attracted by the magnet: glass, wood, copper, nickel, zinc, aluminum, 
paper, tin, and iron. 

Suggestion. Bits of each of the foregoing substances can be kept in a small evaporating dish for use in 
this experiment. 

Conclusion: 


Polarity. Sift some iron filings on a paper over a space as long as your bar magnet. 
Roll a bar magnet in the filings. Pick up the magnet and observe where the filings cling to 
the magnet most abundantly. Place two magnets, with their like poles adjacent, in the filings 

and note results when the magnets are lifted. 

Repeat, placing the magnets with their like poles opposite in the filings, and then observe 

results when the two magnets are lifted. 

Loop a copper wire around the middle of a bar magnet and then suspend it from the 
wooden support so the magnet will be free to turn through a horizontal plane. In what 

position does it finally come to rest? . 

Bring the N-pole of a second bar magnet near the N-pole of the suspended magnet. 
Repeat, holding the S-pole of the magnet near the N-pole of the suspended magnet. In 
exactly the same manner test the S-pole of the suspended magnet with each pole of a bar 
magnet. 

Magnetize a steel knitting needle (full length). Heat the needle with the tip of a flame 
at a point about 2 in. from one end until the heated part of the needle is red hot. Holding 
the needle firmly with two pairs of pliers so the hot portion is between them, twist the 
needle sharply. Repeat with a heated portion near the other end of the needle. When the 
needle is cool, lay it on a paper of iron filings. Where do the filings cling to the needle when 

it is lifted? . Such intermediate poles are 

called consequent poles. 

Conclusion: Summarize the facts you have learned concerning polarity. 


Magnetic Transparency. Sift some iron filings over a sheet of paper. Move the end of 
a bar magnet around underneath the paper. Does the magnet affect the filin gs through the 

paper? .In the same manner test the transparency of sheets of each of the following 

materials: copper, zinc, lead, wood, glass, aluminum, tin, and iron. 


130 







Conclusion: 


Magnetic Induction. Hold one end of a bar magnet in contact with an eightpenny cut 
nail. Dip the other end of the nail in a dish of tacks or brads. What happens when the 

magnet and nail are lifted? . Remove the magnet, and then see 

whether the nail will pick up any tacks. Result?. 

Pick up the nail with the N-pole of the magnet adjacent to the head of the nail and hold 
the other end of the nail near the N-pole of a compass needle. Reverse the nail and test 
again. 

Conclusion: Magnetism may be induced in magnetic material by. 

When magnetism is induced, . polarity is induced in the end nearest 

the magnet, and. polarity in the more remote end. 


131 









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Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 51 —LINES OF FORCE 


Purpose, To make permanent charts of the lines of force about magnets. 

Apparatus; Board, 9x11 in., grooved to hold magnets; two bar magnets; horseshoe magnet with 
armature; iron fihngs; sieve or metal box with perforated cover; pan for iron filings; 
pins; blue print paper. 

Suggestion. Blue-print paper may be bought at little expense, put up in 10 yd. roUs, one yard wide. 
Sketches of the lines of force may be made on blank paper, if blue-print paper is not available. 

Note. When iron filings are brought into the magnetic field of a magnet, each filing 
becomes a small magnet by induction. These filings attract each other and they are mutually 
attracted and repelled by the poles of the permanent magnet. For example, the N-pole of 
each filing is repelled by the N-pole of the magnet, but it is attracted by the S-pole of the 
magnet. Thus the filings arrange themselves in curves along what are called lines of force. 

Method. Put a bar magnet in the grooved board, as shown in Fig. 79. In a part of 
the room where the light is somew^hat subdued, fasten a sheet of blue-print paper (9x11 in.) 

sensitive side up to the board by pinning it at the cor¬ 
ners. Using a sieve or box with perforated cover, sprinkle 
a rather thin layer of iron filings evenly over the surface 
of the paper. Hold the board firmly on the table with 
the left hand and tap it gently with the fingers of the 
right until the filings arrange themselves in the direction 
of the lines of force. Support the board so that the blue¬ 
print paper is exposed to direct sunlight until the paper 
acquires a bronze tint. (Probably about 5 min.) Remove 
the pins, shake the filings off into a pan, and develop the 
print by washing it thoroughly in water. The print must 
be washed until all the yellow color has disappeared. 
Spread the print face downward on a pane of glass to dry. 

In the same manner, make prints showing the lines of 
force about two magnets, laid with like poles adjacent; 
about two magjiets, with like poles opposite; about a 
horseshoe magnet without the armature; and about a 
horseshoe magnet with the arm,Rture, 

Trim the edges of the prints so they will fit in your 
note-book, and label each one carefully. 



133 























Questions. From a study of your prints answer the following questions: 

1. Do the curves appear to be open or closed curves? 

2. Which do you think offers the better path for the lines of force, air or iron? 

3. Do the curves cross one another at any point? 

4. Where do the lines of force appear to be concentrated? 


134 


Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 


DATE_ 

EXP. 52 —VOLTAIC CELLS 


Purpose. To make a voltaic cell and to study its action and its defects. 

Apparatus: Simple demonstration cell, consisting of some type of battery stand, two zinc strips, 
copper strip, and carbon rods or strips. The copper and zinc strips may be cut from 
zinc and copper sheets; they should be about 1x4 in. Voltmeter; enameled pan; 
gravity cell or Daniell cell. The commercial type of cell may be used, or the simple 
demonstration cell which includes a porous cup and cylindrical copper element; amal¬ 
gamating fluid, which is made by dissolving 200 gm. (about 15 c.c.) of mercury in a 
mixture of 175 c.c. of nitric acid and 625 c.c. of hydrochloric acid. The solution may 
be kept in a glass-stoppered bottle and used from year to year until the mercury is 
all exhausted. Annunciator wire. No. 18, for connections. 

Note. When two unlike elements are immersed in a fluid which acts upon one of them 
and not upon the other, or upon one of them more rapidly than upon the other, a voltaic 
cell is formed. One of the plates will have a higher potential than the other, due to the chemi¬ 
cal action, and an electric current will flow when the elements are joined by a conductor. 
While almost any combination of elements and a large variety of solutions can be used for 
voltaic cells, yet zinc has been found to be the most satisfactory element for the negative 
plate, and carbon for the positive plate. So feeble an acid as carbon dioxide dissolved in 
water will dissolve iron quite rapidly when carbon is in contact with the iron. Iron pipes 
rust out very quickly when laid in concrete containing cinders (carbon). 

ONE-FLUID CELL 

Method. Local action. Put a strip of zinc in a tumbler one-third full of sulphuric acid, 
1 part of acid to 20 parts of water. The bubbles that rise are hydrogen. Since zinc is an 
element, the bubbles must come from the acid. Sulphuric acid is composed of hydrogen, 
sulphur, and oxygen. Its chemical formula is H2SO4. As the hydrogen is set free, the zinc 
goes into solution. What is the color of the zinc after a couple of minutes? ...... This 

color is due to carbon impurities in the zinc. Coke, a form of carbon, is used in extracting 
zinc from its ores, and some of the excess carbon is left in commercial zinc. Since these carbon 
particles are not acted upon by the acid, they set up miniature cells in the liquid, thus 
wasting energy. The defect is known as local action. 

Amalgamation. Dip one end of the zinc strip into a tumbler two-thirds full of amalga¬ 
mating fluid. After about a minute remove the strip, rinse it with water, and wipe it dry. 

What is its appearance? . 

Put the amalgamated strip in the tumbler of sulphuric acid. Do you observe any action? 

. Does any carbon appear at the surface? . What is the remedy for local 

action? . 


135 












Study of the 'positive plate. Remove the strip of amalgamated zinc from the acid, rinse 
it, and lay it in the enameled pan. Take care not to get any acid on your clothing or on the 
table. Always rinse the strips when they are removed from the acid and keep them in the enameled 

pan. Insert a strip of copper. Does the acid act upon 

the copper? .Replace the copper with a carbon rod 

or strip. Is there any action?. 

Open circuit. While the carbon is still in the acid, 
insert the strip of amalgamated zinc, taking care that 
they do not touch each other. Is there any apparent 

action while the cell is on open circuit? . 

Closed circuit. Remove both strips from the acid, 
rinse them and wipe them dry. Place them in the 
clamps of the battery stand, Fig. 80, and join their 
terminals to a voltmeter. Then place the clamps on 
the tumbler so the elements dip into the acid. Read 

the voltmeter. Voltage, . Observe the action in 

the cell. Where do bubbles of hydrogen appear to be 

liberated*^ . 

Polarization. Short-circuit the cell for 2 or 3 min. 
by pressing a heavy copper wire against the ends of the 
plates. Remove the copper wire, and then read the volt¬ 
meter. Voltage . What is the appearance of the 

positive plate? . This substitu¬ 

tion of a hydrogen plate for the carbon plate is called polarization. Hydrogen and zinc 
do not furnish as high a voltage as carbon and zinc, hence polarization is a defect. Lift 
the clamp and wipe the bubbles of hydrogen frojn the positive plate. Does the voltage 

rise to its first value?.Short-circuit the cell again until it is polarized. Add a few 

crystals of chromic acid or sodium dichromate to the acid in the tumbler, and stir the acid 
to facilitate solution. What is the effect on the voltmeter reading as the crystals go into 

solution? . These crystals are oxidizing agents which oxidize the 

hydrogen bubbles, forming water. How is the constancy of the cell affected by the addi¬ 
tion of the crystals? . Should a one-fluid cell be kept on open 

or closed circuit? . 



Fig. 80 


136 





















TWO-FLUID CELL 

Note. The gravity cell may be used in this experiment. See Fig. 81. In such a cell 
the copper plate is at the bottom of the jar immersed in a nearly saturated solution of copper 
sulphate. The zinc plate is suspended in a dilute solution of sulphm’ic acid or zinc sulphate 
which floats upon the denser solution of copper sulphate. The chemical action is the same 
as in the Daniell cell. The cell is cheaper than the Daniell and easier to keep in order. 



Fig. 81 Fig. 82 


Daniell cell. Fill the porous cup half full of sulphuric acid (1-20), and immerse in it 
an amalgamated zinc plate. Place the porous cup in the glass jar, and put the copper cylinder 
in the jar so that it surrounds the porous cup. Fig. 82. Then fill the jar with a nearly 
saturated solution of copper sulphate to the level of the hquid in the porous cup. Let the 
cell stand for a few minutes until the liquids have thoroughly wet the porous cup. It is a 
good idea to let the porous cup stand for some time in water before beginning the experiment. 


Connect the cell to a voltmeter and take the reading. Voltage . Short-circuit the cell 

for 3 min., and again find its voltage.Does this cell polarize?.Lift the copper 


element from the liquid and examine it. What appears to have been deposited on the copper 


plate? . In this cell the chemical action is as follows: 

hydrogen + copper sulphate-^ hydrogen sulphate + copper. 

H2 + CuS 04 -> H2SO4 + Cu 


No hydrogen reaches the positive plate. Does the fact that copper is deposited on the copper 

plate suggest a reason for the constancy of the Daniell cell? . 

When the Daniell cell is not in use it should be connected with a resistance of about 40 ohms. 


137 



































Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE_ 


EXP. 53 —E.M.F. AND AMPERAGE OF CELLS 


Purpose, (a) To show that the voltage (E.M.F.) of a cell depends only upon the materials 
used in its construction. 

(b) To show that the amperage varies with the materials, the size of the plates, 
and the distance between them. 

Apparatus: Demonstration cell as used in Exp. 52; sulphuric acid, 1-20; strips of carbon, copper, 
iron, lead, zinc, and aluminum; voltmeter; ammeter; and No. 18 insulated wire for 
connections. 

Note. In Exp. 52 we learned that different kinds of material may be used for making 
voltaic cells. But cells vary in voltage and in internal resistance, and some cells polarize 
readily. By Ohm’s law, we know that the amperage increases as the voltage increases, and 
increases as the resistance decreases and vice versa. Therefore, to study the merits of a cell, 
we must learn something about its voltage and its amperage. 

VOLTAGE OF CELLS 

Method. Materials. Use the demonstration cell apparatus that was used in Exp. 52. Fill 
the tumbler one-third full of sulphuric acid, 1-20. Clamp in position strips of carbon and of 
zinc. Test the voltage. In the same manner, find what voltage is given by each of the follow¬ 
ing combinations and record in the table: carbon and copper; carbon and iron; carbon and 
lead; carbon and aluminum; copper and iron; copper and lead; copper and zinc; copper 
and aluminum; lead and iron; lead and zinc; lead and aluminum; iron and zinc; and iron 
and aluminum. Use fresh acid and wipe the plates dry for each trial. 

Data. 


Positive 

element 

Negative 

element 

Voltage 

Positive 

element 

Negative 

element 

Voltage 

Positive 

element 

Negative 

element 

Voltage 

Carbon 

Zinc 


Copper 

Iron 


Lead 

Zinc 


Carbon 

Copper 


Copper 

Lead 


Lead 

Aluminum 


Carbon 

Iron 


Copper 

Zinc 


Iron 

Zinc 


Carbon 

Lead 


Copper 

Aluminum 


Iron 

Aluminum 


Carbon 

Aluminum 


Lead 

Iron 






139 























Size of 'plates. Connect a Daniell cell to a voltmeter. Note reading. Lift the zinc 
prism nearly to the surface of the acid. This gradually reduces the size of the plate. How 

does lifting the plate affect the voltage? . Repeat the experiment, 

gradually lifting the copper plate. Result? . Try lifting both 

plates at once. Result? . What do you conclude concerning the 

effect of the size of the plates of a cell upon its voltage? . 

Distance between plates. Move the plates nearer together and then separate them as 
far apart as possible. Draw a conclusion concerning the effect upon its voltage of the distance 
between the plates of a cell. 


AMPERAGE OF CELLS 

Method. Connect the terminals of a Daniell cell to an ammeter. Take the reading. 

Amperage, . Lift one of the plates nearly to the top as before. 

Repeat by lifting the other plate. How does the size of the plates affect the amperage? 

Bend the copper plate so it will fit the porous cup more closely, thus bringing the plates 

nearer together. How is the amperage affected? . 

Conclusions: The voltage of a cell depends upon . 

.; it is independent of . 

The amperage of a cell is increased by . 

. and . 

Questions. 1. What elements are used in making a dry cell? \^Tiat is the usual voltage 
of a dry cell? The usual amperage? 


2. What is the advantage of large plates in a cell? The disadvantage? 


140 

















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 


DATE_ 


EXP. 54 —GROUPING CELLS 


Purpose. 


(a) To learn how cells should be grouped to secure the highest voltage. 

(b) To learn what grouping gives the highest amperage: (1) when the external 
resistance is large; (2) when the external resistance is small. 

Apparatus: Three gravity or Daniell cells; voltmeter; ammeter; resistance coils; brass connectors; 
No. 18 wire. 


Note. Either Daniell or gravity cells should be used for this experiment, since they 
are non-polarizing. It often happens that a single cell does not yield high enough voltage 
for the work desired, or that it does not give enough current. In such cases cells may be 
grouped. When the positive element of one cell is connected to the negative of the next, and 
so on, the cells are said to be grouped in series. The current flows through all the cells in 
turn. When the positive element of one ceU is connected to the positive of another, and the 

negative of the first to the negative of the 
second, the cells are said to be grouped in 
multiple, or parallel. It is possible also to 
have a mixed grouping, part in series, and 
then two or more series joined in multiple. 

Method. Connect a single gravity (or 
Daniell) cell to a voltmeter and take the 
reading. Find what amperage the cell will 
give when connected directly to an ammeter, 
and when it is connected to an ammeter in 
series with a resistance of 40 ohms. 

Connect three gravity (or Daniell) cells in 
series. (Join the positive terminal of one cell 
to the negative of the next, or copper to zinc, 
etc.) Connect the terminals of the outside 
cells to a voltmeter. Record the reading. Next connect them in series with a resistance box 
and an ammeter, as in Fig. 83. Introduce 40 ohms resistance and take the ammeter reading. 
In this case the external resistance is much larger than the total internal resistance of the cells. 
Next connect the cells directly to the ammeter to find what current flows when the external 
resistance is very small. (The ammeter resistance is probably not more than 0.001 ohm.) 

Repeat the experiment, exactly as before, but connect the three cells in multiple or 
parallel. Join the copper of one cell to the copper of the next, and so on. In the same 
manner connect the zinc elements. 



141 






























Data. 


Grouping 

Voltage 

Maximum current 

Current with 

40 ohms resistance 

Single 




Three ceils 
in series 




Three cells 
in parallel 





Draw diagrams to show (1) the best method of connecting cells when the external re¬ 
sistance is large compared with the internal resistance; (2) when the external resistance is 
smaller than the internal resistance. 



Questions. 1. It needs nearly 2 volts to plate an object with copper. How would you 
connect cells for this purpose? 

2. Can you make a general statement which covers the directions for the best method 
of grouping cells? 


142 













Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 56 —LAWS OF RESISTANCE 


Purpose. To measure the resistance of conductors by the voltmeter-ammeter method. 

Apparatus; Voltmeter (0-10); ammeter (0-5, or 0-15); resistance box; battery of 5 or 6 volts; No. 18 
wires for connections; board as described; spools of wire of unknown resistance. 

Suggestion. A very convenient board for permanent use may be made as follows; Near one end of a 
10 X 12 in. board fasten two 3-connection binding posts at A and B, about 3 in. apart. At C and D, Fig. 84, 
fasten two 2-connection binding posts. Fasten a knife switch at K, and connect its terminals to A and C 
with No. 14 insulated copper wire. The laws of resistance are all exemplified by using the following coils of 
wire: 40 cm. spool of No. 30 German silver (nickel silver); 200 cm. spool of No. 30 German silver; 200 
cm. spool of No. 27 German silver; 2000 cm. spool of No. 30 copper. 

Note. Just as some substances transmit heat better than others, so some materials are 
better conductors of electricity. In general, the metals are good conductors, but some metals, 
silver and copper for example, are much better conductors than iron, lead, German silver 
(an alloy of nickel, zinc, and copper) or nichrome (an alloy extensively used in electric heaters). 
The student naturally expects that the resistance of a conductor increases with its length, 
but he may not expect to find the resistance decreasing as the diameter increases. 




Method. Connect the apparatus as shown in Fig. 85. Put a low reading voltmeter in 
parallel at V (voltmeters are always connected in parallel, or multiple), so that it will be 
shunted across the spool of wire x whose resistance is to be measured. is a variable rheostat, 

143 





















































or resistance; A is a low reading ammeter which is connected in series with the spool of wire, 
the battery, and the resistance box. 

With the 40 cm. spool of No. 30 German silver wire in series, introduce 5 ohms resistance at 
R and close the knife switch. Gradually reduce the resistance at R until the ammeter reading 
has the desired value. Then read both the voltmeter and the ammeter as exactly as possible, 
estimating to tenths the smallest scale divisions. The voltmeter gives the fall of potential 
across the terminals of the wire, and the ammeter shows the amount of current flowing 

,, u T) . 1 • . /IN potential difference (volts) ^ ^ 

through it. By Ohm s law, resistance (ohms) = -^^. Compute the 

current (amperes) 

resistance of the coil. 

Substitute for the coil just used, each of the other coils in turn and measure their resist¬ 
ances. 


Data. 


Material 

Gauge No. 

Length 

Diameter 
(mils) 

Diameter 

squared 

Volts 

Amperes 

Resistance 










































Calculations: 


Conclusions: The resistance of a conductor 



















Questions and problems. 1, You will note that the cross-sectional area of No. 27 wire 
is just double that of No. 30. How does doubling the area of cross-section affect the resist¬ 
ance? What is the effect of doubling the length? 


2. How many feet of No. 27 G.S. wire will be needed to have the same resistance as 
20 ft. of No. 30 copper wire? 


145 


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Laboratory Exercises in Physics 
Chables E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 66 —LAWS OF RESISTANCE 


Purpose. To measure the resistance of conductors by the Wheatstone bridge method. 

Apparatus: Wheatstone bridge; dry cell; “dead-beat” galvanometer; resistance box; spools of wire 
of unknown resistance. See suggestions under Exp. 55; wires for making connections, 
not smaller than No. 18. 


Note. See Exp. 55. 



Fig. 86 


Method. Set up the apparatus as shown in Fig. 86. See that all contact points are 
clean and bright, and use as short pieces of wire as possible for connectors. Put a 40 cm. 
spool of No. 30 German silver wire at x, put the resistance box at R, and the galvanometer 
at G. Of course the total length of wire used for connecting the dry cell to the terminals A 
and C must be a little more than one meter. A very short piece of wire may be used to 
connect one terminal of the galvanometer to the contact screw D, but the piece connecting 
the other terminal with the sliding contact K must be about 50 cm. long. 

Introduce a resistance of 2 ohms at R, and press the contact key K when it is near 
the middle of the bare wire which is stretched across the Wheatstone bridge. If the galva¬ 
nometer needle is deflected, there is a difference of potential between K and D. Move the 
sliding contact until you find a point on the wire where no deflection of the needle is produced 
upon closing the key. This may be done quite quickly by using the following method. 
Suppose the needle is deflected in one direction when the key is at the 40 cm. division, and 
in the other direction when the key is at the 60 cm. division. Then the point of zero poten- 

147 






































tial difference is some place between these divisions. Next try the 45 and 55 cm. divisions. 
If the direction of the deflections is opposite, the point sought is between 45 and 55 cm. If 
the deflection is the same direction for both, but opposite to that obtained at the 60 cm. 
position, then the point is between 55 and 60. In this manner, a student will soon be able 
to find a zero deflection position for K very quickly, by gradually narrowing the distance 
between two positions where the deflection is opposite. Record the length I, and the length 
V. The resistance x is found by use of the following formula: RV = xl. Change the value 
of the resistance at R, and take a second trial, using the same spool of wire. If possible, 
always use such a resistance that the position of K will fall between the 40 and 60 cm. 
divisions when the bridge is balanced. 

In the same manner, find the resistance of each of the other spools of wire, taking two 
trials for each and using a different resistance for each trial. 


Data. 


Trial 

Material 

Gauge No. 

Length 

Diameter 

Diameter 

squared 

Length 

1 

Length 

1 ' 

Resistance 

R 

Resistance 

X 

1 










2 










1 










2 










1 










2 










1 










2 

- 










Calculations: 


Conclusions: The resistance of a conductor 






















Questions and problems. 1. A wire 10 ft. long has a resistance of 20 ohms. Find the 
resistance of a wire 20 ft. long, but of twice the diameter of the first wire. 


2. For a high resistance, would you use: (1) copper or German silver? 
or a thick one? (3) a long wire or a short one? 


(2) a thin wire 


149 



* m '■ ,0 

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^ -t 

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4 





4 


» 










Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 57 —SERIES AND SHUNT RESISTANCE 


Purpose. To measure the resistance of conductors joined (1) in series; (2) in parallel, 
or multiple. 

Apparatus: Same as for Exp. 56. 

Note. When coils of wire are joined in series, the current must flow through each coil 
in turn. The combined resistance would therefore be the sum of all the separate resistances. 
When conductors are joined in parallel, the current divides; part flows through each branch of 
the circuit. In heavy traffic, parallel streets would offer less congestion than a single street. 
From similar reasoning, we may expect that the total resistance of two or more conductors in 
parallel is less than the single resistance of any one. 

Method. Set up the apparatus just as you did in Exp. 56. Join the 40 cm. spool of No. 30 
German silver wire and the 200 cm. spool of No. 30 German silver with a brass connector and 
then measure their combined resistance just as you did in Exp. 56. Take two trials, using 
different resistances at R, Fig. 86. 

Then join the same coils in parallel and measure their combined resistance. The conduct¬ 
ance of a coil may be defined as the reciprocal of its resistance; the conductance is inversely 

proportional to the resistance. By formula, conductance = -. Find the conductance of 

r 

each coil by dividing 1 by its resistance as found in Exp. 56. Carry two decimal places. Com¬ 
pute also the total conductance of the two coils in parallel by dividing 1 by the resistance as just 
found. This total conductance should equal the sum of the separate conductances. Suppose 
w'e let r represent the resistance of one single conductor, r' the resistance of the other single 

conductor, and R the resistance of the two conductors in parallel, then 4 = " + V 

R r r 

Whence R = 

T T 

Repeat the experiment, using the 200 cm. spool of No. 30 German silver wire in parallel 
with the 200 cm. spool of No. 27 G.S. wire. Measure the resistance, and compare it with the 
resistance as computed from the above formula. Substitute for r and r' the values obtained 
in Exp. 56. 


151 







Data. 


Connection and 
material 

Length 

1 

Length 

1' 

Resistance 

R 

Resistance 

X 
































Calculations: 


Problems. 1. Three conductors are joined in series; their resistances are 3, 4, and 5 
ohms respectively. Find their joint resistance. Draw a general conclusion concerning the 
joint resistance of conductors in series. 


2. Find the joint resistance of the three conductors of Problem 1 when they are joined 
in parallel or multiple. 


152 



















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 58 — TEMPERATURE AND RESISTANCE 


Purpose. (a) To show how an increase in temperature affects metallic conductors and 
non-metallic conductors. 

(6) To find the temperature coefficient of the resistance of some metal. 

Apparatus: All the apparatus as used for the Wheatstone bridge Experiment, No. 56; temperature 
resistance coil, preferably of copper; calorimeter; burner; boiler; 32-C.P. carbon lamp; 
40-watt tungsten lamp; board, with fuses and knife switch as described. 

Suggestion. For measuring the hot resistances of the lamp filaments one board made as follows is 
sufficient for the entire class. On a board for permanent use mount binding posts and fuse plugs and sockets 
as shown in Fig. 87. The binding posts A and B are to be connected to a 110-volt circuit when the board 
is in use. At F and F' mount two sockets which are to be fitted with 6-ampere fuse plugs. A is a knife 
switch, and S a lamp socket. The binding posts C and D are connected directly to the lamp socket, and a 
voltmeter is shunted across the socket. An ammeter is connected in series with the circuit by means of the 
binding posts X and Y. Use No. 17 insulated wire for making the connections. 


Note. Resistance coils serve two purposes in electrical circuits. In some cases they 
are used to lower the potential and thus reduce the current to the desired amperage. They 
are also used as measuring instruments. Since the resistance of most metals varies with the 
temperature, the temperature coefficient of resistance has a very important bearing upon the 

quality of the resistance coil. In making re¬ 
sistance boxes, special high resistance material 
which is little affected by temperature is chosen. 

Method. Set up the Wheatstone bridge 
apparatus just as in Exp. 56. Fill the calo¬ 
rimeter two-thirds full of cold water and im¬ 
merse the temperature coil whose resistance 
is to be measured in the water. Read the 
temperature of the water, and measure the 
resistance of the coil of wire. 

Next measure the resistance of the coil 
when it is immersed in boiling water. Record 
the temperature of the water. 

Divide the increase in resistance in ohms 
by the increase in temperature in degrees 
Centigrade to find the increase in resistance per degree. Dividing the quotient thus obtained 
by the resistance of the cold coil gives the temperature coefficient of resistance of the metal. 
The temperature coefficient of resistance of a metal may he defined as the increase in the resistance 
of 1 ohm of that metal when heated 1° C. 



Fig. 87 


153 



































By the use of the Wheatstone bridge, measure the resistance of the cold carbon lamp and 
the cold tungsten lamp. 

Connect a commercial voltmeter (0-150) to the binding posts C and D of the board 
described under the suggestion. The ammeter, which should have a range of 10 amperes, is 
connected to the terminals X and Y. Screw the tungsten lamp into the socket S and close 
the knife switch. Read the voltmeter and the ammeter, and compute the resistance of the 
hot tungsten lamp. 

Open the switch, substitute the carbon lamp for the tungsten, and measure its resistance 
in the same manner. 

Data. 


Material 

Temper¬ 

ature 

Length 

1 

Length 

1' 

Resistance 

R 

Resistance 

X 

Lamp. 

Volts 

Amperes 

Resistance 

Coil, 

cold 






Tungsten, 

hot 




Coil, 

hot 






Carbon, 

hot 




Tungsten, 

cold 










Carbon, 

cold 











Temperature coefficient of 

Calculations: 


Questions. 1. Try to find out what material is used for resistance boxes, and why. 


2. Draw a conclusion concerning the effect of an increase in temperature upon metallic 
conductors. Upon non-metallic conductors. 


3. Sometimes when 10 or 12 tungsten lamps on the same circuit are all turned on at 
once, a fuse will blow out. Explain. 


154 


















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 59 —DIVIDED CIRCUITS 


Purpose, To show how the current is distributed over the branches of a divided circuit. 

Apparatus: Three ammeters (0-10); three rheostats, 5 amperes capacity; battery of about 6 volts; 
contact key. 

Suggestion. Since this experiment calls for three ammeters and three resistance boxes, the expense of 
the apparatus is too great for use with individual students. It may be performed as a group experiment. 

Note. In the experiment for measuring shunt resistances, we compared the lowered 
resistance by the use of parallel circuits to the relief of traffic congestion by the use of parallel 
streets. If the streets have the same width, we may assume that each will carry half the 
traffic. If they are of unequal width, we may assume that more traffic will follow the line 

of least resistance on the broader street. With 
parallel circuits in electric wiring, we expect each 
of two branches to carry half the current, if the 
resistance of each branch is the same. If one 
wire has a higher resistance than the other, we 
may expect that less current will flow through this 
branch. The bulk of current follows the line of 
least resistance. 

Method. Set up the apparatus as shown in 
Fig. 88. The battery may be a storage battery, 
or three or four dry cells in series. The ammeters 
B and C are connected in series with the rheostats R' 
and R" respectively. The ammeter A is joined in 
series with the rheostat R. Set the rheostats R' 
and R" at zero, and introduce the maximum re¬ 
sistance at R. Close the switch at K and gradually 
decrease the resistance at R until the ammeter A shows a reading of 4 or 5 amperes. Do the 

two ammeters at B and C show the same reading? . Does the sum 

of the ammeter readings B and C equal the reading of ammeter Af . 

Introduce a small resistance at R' and an equal amount at R". Record the readings of 
all three ammeters and all the rheostats. 

Change the resistance at R" until it is twice that of R' and again read all the ammeters 
and resistances. 

Take two more trials, making the resistance at R" three times and then four times as 
much as that at R'. 



155 


















Data. 


Trial 

Ammeter 

A 

Ammeter 

B 

Ammeter 

C 

Sum of 

B and C 

Resistance 

R 

Resistance 

R' 

Resistance 

R" 

1 








2 








3 








4 









Questions and problems. 1. How does increasing the resistance in one branch of a 
circuit affect the amount of current flowing through that branch? How does it affect the 
amount of current flowing through the other branch? 


2. Two branches of a divided circuit have resistances of 5 and 9 ohms respectively. If 
10 amperes of current flow through the main circuit, how many amperes will flow through 
each branch? 


156 
















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME_ 

DATE_ 


EXP. 60 — INTERNAL RESISTANCE OF CELLS 


Purpose. To measure the internal resistance of a cell (a) by the voltmeter-ammeter 
method; (6) by the reduced deflection method. 

Apparatus: Voltmeter, low range; ammeter, low range; switch; resistance box; dry cell; Daniell cell, 
or gravity cell; No. 30 G.S. or No. 27 nichrome wire. 

Note. In applying Ohm’s law to battery circuits we must always consider the internal 
resistance of the battery and the external resistance of the circuit. In passing through the 

electrolyte in the battery or cell, an electric current is 
opposed by a certain amount of resistance which varies 
with the size of the plates, the distance between them, 
and the nature of the electrolyte. If a gravity cell has 
an E.M.F. of 1.1 volts and its internal resistance is 1 ohm, 
then the maximum current which such a cell can furnish 
(when the external resistance is zero) is 1.1 amperes. If 
a dry cell has an E.M.F. of 1.5 volts, and an internal 
resistance of 0.05 ohm, then the maximum current which 
such a cell can furnish is 30 amperes. 

Method. Connect the gravity or Daniell cell in 
series with a switch, ammeter, and resistance box as 
shown in Fig. 89. Connect a voltmeter across the 
terminals of the cell. 

With the switch open, take the reading of the 
voltmeter, calling the value E. No resistance need be 
used with this type of cell. Set the resistance box at zero. 
Close the switch and read both the voltmeter and the 
ammeter. Call this reading of the voltmeter E', and the ammeter reading I. The resist¬ 
ance of the cell, r, may be found by the following formula: 

E - E' 
r = -. 

I 

Repeat the experiment, using the dry cell. Introduce a small resistance before closing 
the switch, so the ammeter reading will not be excessive. 



157 























Data. 


Type of cell 

E 

E' 

1 

R 

r 




















Reduced deflection method. Connect the gravity cell, the ammeter, and the resistance 
box all in series. Without any resistance introduced, take the ammeter reading. Then 
introduce gradually just enough resistance to reduce the ammeter reading to exactly one-half 
what it was before. The internal resistance of the cell is the same as the reading of the 
rheostat. 

Internal resistance of gravity cell,. 

If the resistance of the dry cell is to be measured by this method, an ammeter of at least 
30 amperes capacity must be used, or a low resistance shunt may be connected across the 
ammeter terminals. 

Caution. Do not hum out your ammeter. Find the internal resistance of the dry cell by the reduced 
deflection method. If a resistance box of sufficient capacity is not available, use just enough German silver 
wire (No. 30) or nichrome No. 27 in series with the ceU and ammeter to reduce the ammeter reading to one- 
half. Then measure the length of wire used and calculate its resistance. 

E 

In the formula, I = -, we assume that R, the external resistance, is zero when we 

R + r 

take the first reading. Then when we increase the external resistance until I is reduced to 
one-half, of course R and r must be equal. 

Internal resistance of dry cell,. 

Questions. 1. Explain why the reduced deflection method is not very accurate. 


2. Refer to Exp. 53, and explain why decreasing the distance between the plates 
increased the current. 


3. In Exp. 53, why did lifting the plates part way out of the electrolyte reduce the 
current? 


158 















Laboratory Exercises in Physics 
Chables E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE 


EXP. 61 —FALL OF POTENTIAL 


Purpose. To show that the fall of potential along a conductor is proportional to the re¬ 
sistance. 

Apparatus: Battery of dry or storage cells, about 5 or 6 volts; voltmeter, low range; board, one 
meter long, with binding posts as shown in Fig. 91; nichrome wire. No. 24; nichrome 
wire. No. 27. 



Fig. 91 


A B 



Note. Suppose we have two tanks connected by a pipe fitted with a stop-cock K as 
shown in Fig. 90. If the tank A is full of water and B is empty the difference of pressure 
(potential) is equal to the depth of the water in A. When the stop-cock is opened a little, 
we reduce the resistance slightly, and the difference in pressure is correspondingly reduced. 
The difference in pressure falls more rapidly as the stop-cock is opened more widely. In 
an analogous manner, the difference in electrical pressure is greater when the resistance is 
high, and the potential difference decreases as the resistance is reduced. 

Method. Connect the apparatus as indicated in Fig. 91. Between the binding posts 
A and B stretch one meter of No. 24 nichrome wire. Between C and D stretch one meter of 
nichrome wire. No. 27. Join three dry cells in series and connect their tenninals to the 
binding posts A and B, using No. 18 copper wire. Using a short copper wire, join the plus 
terminal of a voltmeter to the binding post A; the other terminal of the voltmeter should 
be connected to a copper wire nearly one meter long. Press the end of this wire firmly against 
the nichrome wire at the 25 cm. mark. Record the reading of the voltmeter. Take readings 
when the end of the wire is pressed successively against the nichrome wire at the 50 cm., 
75 cm., and the 100 cm. mark. 

Connect the cells to the terminals C and D. Attach the plus terminal of the voltmeter 
to the post C and take voltmeter readings when the other terminal is pressed successively at 
the 25 cm., 50 cm., 75 cm., and 100 cm. marks. 

159 
































Join B and D with a heavy copper wire and connect the cells to the binding posts A 
(+) and C {—). Find the fall of potential along one meter of No. 24 wire (between A and B) 
and also along one meter of No. 27 wire (between C and D). 

Data. 


Wire 

Gauge No. 

Potential 

difference 

Length 










































Questions. 1. How does the fall of potential vary with the length of a uniform con¬ 
ductor? 


2. When the wires are joined in .series, does the voltmeter show a greater potential 
difference between A and B (No. 24 wire) or between C and D (No. 27 wire)? 


3. No. 24 wire has just twice the cross-sectional area of No. 27. How does the fall of 
potential vary with the resistance of the conductor? 


160 

















Laboratory Exercises in Physics 
Charles E, Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 62 —MAGNETIC FIELD ABOUT A CONDUCTOR 


Purpose. To study the effects of the magnetic field which is set up around vertical and 
horizontal conductors. 

Apparatus: Gal\Tinoscope, with binding posts for single turn, a few turns, and many turns of wire; 

wooden block, as shown in Fig. 95; brass connectors; gravity cell; battery of 2 dry 
cells or 1 storage cell; four small compasses. 



Fig. 92 



Fig. 93 


Note. Oersted was the first to show that a current flowing through a conductor pro¬ 
duces a magnetic field around the conductor. A magnetic needle placed near the conductor 
is deflected. Fig. 92. This discovery is a very important one, since it shows the close rela¬ 
tionship between electricity and magnetism. It also paved the way for the development of 
the electro-magnet and the galvanometer. 

HORIZONTAL CONDUCTORS 

Method, (a) Place the galvanoscope on the table so the single wire will be directly 
above the compass needle as it points North and South. See Fig. 93. Turn the compass 
until the N-pole is directly above the zero mark of the scale. Connect a gravity cell to the 
binding posts in such a manner that the current will flow from South to North over the 
needle. Note the direction in which the N-pole of the needle is deflected and the number 
of degrees. Hold the right hand palm downward over the needle with the thumb pointing 
in the direction in which the N-pole is deflected; the extended fingers point in the direction 
of current flow. 

(b) Reverse the direction of the current flow, and again note the direction and amount 
of deflection of the N-pole of the needle. Hold the right hand over the wire as before with 
the thumb pointing in the direction of the deflection of the N-pole. Do the fingers point in 

161 










the direction of the current flow? . Complete the following state¬ 

ment: Imagine that you are swimming with the electric current, facing the magnetic needle, 

the extended left arm points . 

Does this rule apply when the conductor is beneath the needle? . 

(c) Keeping the galvanoscope in the same position, move the compass until it is directly 
beneath the coil of a few turns. Connect the gravity cell to the proper binding posts and 
close the contact key. Record the direction and, the amount of deflection. 

(d) Repeat the experiment, using the coil of many turns. 

Data. 


Coil 

Current flow 

Direction of deflection 

No. of degrees 

Single loop 

Sto N 



Single loop 

NtoS 



Few loops 

Sto N 



Few loops 

NtoS 



Many loops 

Sto N 



Many loops 

NtoS 




Questions. 1. What is the effect of increasing the number of turns upon the amount 
of deflection? 

2. Can the deflection ever reach 90°?.Explain. 


^ 1 

[ ^ 

A 1 

s 1 

1 


r-^ 


Fig. 94 


3. How would you make a very sensitive galvanoscope? 
What do you think would be the effect of having two needles 
of nearly equal magnetic strength fastened together as shown 
in Fig. 94, and suspended between the coils of a galvanoscope 
by means of a very fine thread? Such a combination is called 
an astatic needle. 


162 



















VERTICAL CONDUCTOR 


Method. Midway between the two edges and 1| in. from the end of a block of wood 
6 X 3 X 1| in. bore a hole | in. in diameter. Insert a No. 12 bare copper wire through the 
block and let it extend above the block a few inches. Make a little 
groove along the lower side of the block for the wire, which should be 
bent over and fastened in this groove with a couple of small copper or 
brass staples. Place the block on the table and put four small com¬ 
passes around it as shown in Fig. 95. Connect two dry cells in series 
with the heavy wire so the current will flow up through the wire when 
the contact key is pressed. Note the position taken by the needles and 
make a sketch diagram to show the direction taken by the N-poles. Re¬ 
verse the direction of the current flow, and again sketch the direction 
indicated by the N-poles of the needles. Sketch in the proper square the 
four compasses, showing the position of the needles when no current is 
Fig. 95 flowing through the circuit. 



No current Current flowing upward Current flowing downward 

From a study of your diagrams make a right hand rule that will show the direction of 
the current flow in relation to the direction of the deflection of the N-poles of the needles. 


163 










Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE 


EXP. 63 — ELECTRO-MAGNET 


Purpose. To study the electro-magnet. 

Apparatus: Wooden and iron rods for magnet cores; No. 22 insulated copper wire; brass connectors; 

contact key; dry cell; tacks or small nails; compass needle; rubber tubing, | in. in¬ 
ternal diameter, cut up into f in. lengths; resistance box. 

Suggestion. From a hardware store secure some dowel rods and some iron rods in. in diameter. 
Saw up the dowel rods into 4 in. lengths. The hardware dealer will probably have a metal shear which can 
be used for cutting up the iron rod into 4 in. lengths. 



vms 


Note. In Exp. 62 we learned that a current flowing through a conductor sets up a 
magnetic field around the conductor. If we wind the wire into a loop, all the lines of force 
of such a magnetic field will flow through the loop in the same direction. Therefore the loop 
will have polarity. Just as increasing the number of turns increased the deflection of the 
needle, so increasing the number of turns in a loop increases the strength of its magnetic 
field. In our experiments on the study of the magnet, we learned that iron offers an 
excellent path for lines of force. By winding the turns of wire on an iron 
core we produce an electro-magnet. 

Method, (a) Wind a short piece of wire into a loop about f in. in 
diameter and connect the ends of the loop in series with a dry cell and 
contact key. Fig. 96. Close the key and test 

the loop for polarity. • 

Such a loop is merely a disc magnet. If we 
continue to increase the number of loops, we 
produce the same effect that one would produce 
by piling up disc magnets one upon another. 

Fig. 97. 

(6) Cut a piece of No. 22 insulated copper wire about 3 meters long, 
of rubber tubing over one end of one of the wooden rods so that it will hold one end of the 
copper wire as shown in Fig. 98. Leave a few inches at the end for making connections. 
Taking care not to kink the wire, wind 30 or 35 turns on the wooden rod and fasten the 
other end with rubber tubing as before. Connect the helix you have thus made in series 
with a contact key and dry cell. Test it for polarity when the key is pressed momentarily. 
Do not keep the circuit closed except when tests are being made. Grasp the coil with the 
fingers of the right hand encircling it in the direction the current flows. To which pole 

does the extended thumb point?. As you look at the N-pole of 

the helix, does the current encircle the loop in a clockwise or counter-clockwise direction? 

. Test the helix to see whether it has enough magnetism to pick 

up any tacks. Result? ... 

165 



Fig. 97 


Slip a short piece 
















(c) Remove the rubber fastenings. The coil will then be loose enough so it may be slid 
off the wooden rod without unwinding it. Insert the iron rod in the same coil, tighten it and 
fasten the ends with rubber tubing as before. Connect with the dry cell, contact key, and 
resistance box and test its polarity. Set the resistance box at zero and see how many nails or 

tacks the magnet will pick up. Introduce 0.1 ohm resistance and 

repeat the experiment. Repeat again, using 0.2 ohm resistance. 

(d) Wind 25 or 30 more turns of wire upon the iron core and repeat the experiment as 

it was performed in Record the number of tacks picked up: resistance box at zero. 



Fig. 98 

. ; resistance box at 0.1 ohm, .; resistance box at 0.2 ohm. When 

through with the experiment, slip off the rubber bands, remove the iron core, straighten the 
wire, and wind it into a neat coil around three fingers of the left hand. Fasten the ends 
and return the wire to the instructor. 

Conclusions. State the effect (1) of the iron core on the strength of the magnet; (2) 
of increasing the number of turns; and (3) of increasing the strength of the current. 


Give methods of finding the polarity of an electro-magnet (1) when the direction of the 
current flow in the coil is known; (2) when you have given a small compass needle. 


166 








Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 64 —ELECTRIC BELL AND SOUNDER 


Purpose. To study the telegraph sounder and the electric bell as applications of the 
electro-magnet. 

Apparatus: Two bells; sounder; key; magnetized needle; dry cell; two push buttons; No. 18 annun¬ 
ciator wire. 

Note. Since the electro-magnet is a magnet wliile the current flows through its coils, 
but loses its magnetism as soon as the circuit is broken, it has many applications. The 
telegraph sounder becomes a magnet as the current flows through its coils while the operator 
presses a contact key. It loses nearly all its magnetism when the circuit is broken. With 
the electric bell a vibrator opens and closes the circuit automatically. 

TELEGRAPH SOUNDER 

Method. Examine the telegraph sounder. See Fig. 99. Of what parts does it consist? 


Trace the current through the sounder when it is connected in series with a dry cell and r 
telegraph key. Test the magnet with the magnetized needle to see whether it has polarity 



Fig. 99 

(1) when the key is closed; (2) when the key is open. Results? . 

How is the armature pulled down to cause the “chck” of the sounder? . 

How is the armature returned to its former position when the circuit is broken? 
What is the purpose of the side lever on the telegraph key of Fig. 100? .... 


167 



















ELECTRIC BELL 


Method. Remove the metal cap from the magnet of the bell. Starting with one binding 
post, trace the current through the bell and back to the other binding post. See Fig. 101. 

Remember that the current may flow through the iron base, but 
it does not go skipping across air-gaps. With the magnetized 
needle test the magnet for polarity (1) when the armature is held 
closely against the ends of the magnets; (2) when it is held away 
from the magnet so that it touches the contact screw. Results? 



Connect two push buttons with the bell and dry cell so that 
either push button will ring the bell when pressed. Make a 
sketch diagram to show how such a combination is wired. 

Connect two bells with a push button and dry cell so that 
one button will ring both bells. Make a sketch diagram to show 
the wiring. 

Beginning with either binding post, trace the current through 
the bell, and describe in detail just what causes the bell to ring. 


168 













Sketch of bell and two push buttons. 


Sketch of two bells and a single push button. 


169 





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Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 65 —ELECTRIC HEATING 


Purpose. (a) To find the cost of heating one quart of water from room temperature to 
the boiling point with an electric heater. 

(6) To test the efficiency of an electric heater under actual working conditions. 

Apparatus: Voltmeter, 0-150; ammeter, 0-10; electric heater; switch; electric cable, for connections; 

quart measure; 2-qt. tea-kettle, same as used in Exp. 35; thermometer; watch; same 
board that was used in Exp. 58. 

Note. The use of electricity for heating purposes has certain advantages. It is clean 
and convenient, but unfortunately at the price ’charged per kilowatt-hour in most localities, 
it is more expensive than other methods of heating. The heater consists of a coil of high 

resistance wire which is mounted in a refractory of some kind. 
Joule learned that the heating effects are proportional to the 
resistance and to the square of the current strength. Since the 
current is the same in all parts of a series circuit, the heater 
itself must be made of high resistance wires. Fig. 102. 

Method. Measure out exactly one quart of water from the 
cold-water faucet, and pour it into the 2-quart tea-kettle. Use 
the board shown in Fig. 87, with the voltmeter connected across 
the terminals of the lamp socket and the ammeter joined in 
series with the knife switch and the electric heater, which 
should be attached to the socket S. Set the tea-kettle of water 
Fig. 102 on the heater, take the temperature of the water and record 

the time. Then turn on the current.. Record the temperature 
and time again when the water just begins to boil. Read the voltmeter and ammeter 
every two minutes during the experiment. From the average voltage and amperage cal¬ 
culate the number of kilowatt-hours of electrical energy used. Compute the cost at the 
current price per kilowatt-hour. Remember that volts times amperes equal watts. 



171 








Data. 

Average 

Voltmeter readings, .; .; .; .; .; .; ..; 

Ammeter readings, .; .; .; .; .; .; .; 

Temperature at the beginning . 

Temperature at end . 

Time at the beginning . 

Ti7ne at the end . 

Time required . 

Watts used . 

Total cost at current price of . ^ per kilowatt-hour . 

Calculations: 


Question. Compare the cost of heating one quart of water by electricity with the cost 
of heating one quart of water by gas as found in Exp. 35. 


Method. Efficiency. Weigh the tea-kettle in grams. Add to it exactly 1000 grams of 
water from the cold-water tap. (One liter.) Stir the water thoroughly, observe its tempera¬ 
ture, and note the time. Set the tea-kettle on the electric heater and turn on the current. 
Read the voltmeter and ammeter every two minutes until the water just starts to boil. Then 
turn off the current, and at the same instant note the exact time and take the temperature 
of the boiling water. 

In the formula, calories = P x R X t x 0.24, substitute the values found and compute 
the number of calories given out by the electric heater. I is the current strength in amperes, 
R, the resistance of the heater, and t, ’the time in seconds. 

Calculate the number of calories absorbed by the cold water and the tea-kettle. Then, 
total calories absorbed divided by total calories furnished by the heater equals the efficiency. 


172 






















Data. 


Voltmeter readings, average 

Ammeter readings, . . .; ...; ...; ...; . ..; . ..; ...; ...; average 

Time at the beginning of the experiment . 

Time at the end of the experiment . 

Number of seconds . 

NumSer of calories liberated . 

Weight of tea-kettle . 

Specific heat of tea-kettle . 

Weight of water . 

Initial temperature .. 

Final temperature .. 

Calories absorbed by the tea-kettle . 

Calories absorbed by the water . 

Total calories absorbed . 

Efficiency of the heater . 

Calculations: 


Problems. 1. An electric heater has a resistance of 22 ohms. Find the cost of using 
the heater on a 110-volt circuit 2 hrs. at lOj/f per K.W.-hr. 


2. How many gm. of water could be heated from 20® to 100® by the heater of Prob. 1? 


173 



















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Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 66 — EFFICIENCY OF LAMPS 


Purpose. (a) To compare the efficiency of carbon and tungsten lamps. 
(6) To study series and parallel wiring. 


Apparatus: Lamp board, as shown in Fig. 103; voltmeter, 0-150; ammeter, 0-10; lamps as follows: 

3 40-watt Mazda lamps; 25-watt Mazda: 100-watt Mazda; 150-watt gas-filled Mazda; 
16-C.P. carbon; and 32-C.P. carbon. 



Note. In Exp. 42 we studied the candle power of different types of lamps. It will be 
of interest to measure the amount of current that flows through the lamps when they are 
in use under actual working conditions. Then we can compute the wattage and find the cost 
per candle power per hour. 

Possibly the student has observed that the lamps on trolley cars are often wired in 
groups of five. The voltage upon which the car operates is probably 550; hence by wiring 
in series, there is a fall of potential of 110 volts across the terminals of each lamp. For 
house wiring, the lamps are joined in parallel on a 110-volt circuit. After performing this 
experiment the student can probably give two good reasons why incandescent lamps are 
generally wired in parallel. 

Method. The lamp-board, Fig. 103, is wired as follows: F and F' are fuse plugs of 6 
amperes capacity used to protect the instruments; B, C, and D are lamp sockets wired in 
parallel, and connected to the main wires by binding posts so the connections may be easily 
changed; is a knife switch; A, an ammeter; and V, a voltmeter, which is shunted across 
the terminals of the lamp socket B. 

Screw a 25-watt Mazda lamp into the socket B, close the switch K) find the amperage, 
and the voltage across its terminals. Open the switch and replace the 25-watt lamp with 

175 

















































a 40-watt lamp of the same kind. Take the readings as before. In the same way, find the 
voltage and amperage when the following lamps are used successively: 100-watt Mazda; 
150-watt gas-filled Mazda; 16-C. P. carbon; and 32-C. P. carbon. Calculate the number 
of watts per candle, and the cost per candle per hour at a price of 10^ per kilowatt-hour. 


Data. 


Kind of lamp 

Volts 

Amperes 

Watts 

Rated 

wattage 

Candle 

power 

Watts per 
candle 

Cost per can¬ 
dle per hour 




•• 






















































Calculations: 


Method. Wiring. Screw a 40-watt- Mazda lamp into the socket B; read the ammeter 
and find the voltage across its terminals. Put another lamp exactly like the first one in 
the socket C. Does the voltmeter still show the same difference of potential between E and 

Hf . Find the difference of potential between M and N. Read the ammeter. How 

does the addition of another lamp affect the ammeter reading? . 


Put another 40-watt lamp in socket D. Find the voltage when the terminals of the volt¬ 
meter are connected at R and S. What is the reading of the ammeter when three lamps 

are connected in parallel? . Loosen the lamp at C; are the lights 

at B and D extinguished?.Open the switch and remove the lamps at C and D. Take 

out the fuse plug F' and screw one of the lamps into its socket. Close the switch and find 

the fall of potential across the terminals of each lamp, between 0 and P, and between E 

and H. What is the fall of potential between 0 and Ef .Take the ammeter reading 

176 























when the lamps are connected in series. Unscrew one of the lamps. What happens to the 
other lamp? . Explain. 

Data. 


No. of lamps 

Connection 

Voltage 

Amperage 

Single 




Two 

Parallel 



Three 

Parallel 



Two 

Series 




Conclusions: 


Questions and problems. 1. Give two good reasons why incandescent lamps are gener¬ 
ally wired in parallel. 


2. When is wiring in series an advantage? 


3. A man uses four 40-watt Mazda lamps an average of 2 hours per day for 30 days 
per month. Find his electric light bill for the month at lOjzl per kilowatt-hour. 


177 



















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Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE 


EXP. 67 — ELECTROLYSIS 


Purpose. (a) To study the electrolysis of water. 

(6) To show the relation of the electrolysis of water to the storage cell. 

Apparatus: Battery stand as used in Exp. 52; two dry cells or two storage cells; 2 carbon rods; 

2 copper strips, 1 in. by 4 in.; 2 lead strips, If x4 in.; voltmeter; ammeter; rheostat; 
electrolytic apparatus, or voltameter. 

Note. According to a theory proposed by Arrhenius, certain compounds in water 
solution dissociate into ions. An ion may be defined as an atom or a group of atoms carrying 
an electrical charge. Metallic elements, including hydrogen, carry positive charges, while 
the non-metals carry negative charges. When we put sulphuric acid (H2SO4) into water, 
the acid dissociates into hydrogen ions (H 2 +) and sulphion (SO4 ~). Each hydrogen ion 

carries a positive charge of electricity; the (SO4) group 
carries two negative charges. If we dip two carbon rods into 
such a solution and pass the current from a couple of cells 

through it, the hydrogen ions are attracted to the rod which 

is connected with the negative terminal of the cells, or the 
cathode; the sulphion is attracted to the positive carbon, or 
to the anode. Therefore hydrogen escapes from the cathode; 
the sulphion has its charge neutralized and attacks the water, 
stealing its hydrogen and liberating oxygen at the anode. 

Chemically, H2O + SO4-> H2SO4 + (O). 

In charging a storage cell, the oxygen does not escape, but 
it combines with the lead to form Pb02, or lead dioxide. Thus 
the two plates are made dissimilar. Two dissimilar plates 
immersed in a fluid which acts chemically upon one of them 
Yig. 104 form a voltaic cell. As such a cell is being discharged, the 

hydrogen which is liberated at the negative plate migrates to 
the positive plate and combines with the oxygen of the lead dioxide, thus reducing the 
plate again to metallic lead. 

Method, (a) If a voltameter is available, fill it with water containing a little sulphuric 
acid; connect it in series with 2 dry cells or 2 storage cells and pass the current through 
the electrolyte for a few minutes. 

Suggestion. A half-bottle fitted up with test tubes as shown in Fig. 104 may be used instead of the 
more expensive type of apparatus. Carbon rods may be used instead of platinum. 

When the tubes are f ull of gas, remove them and test the gas. The hydrogen, which is 
liberated at the cathode, burns with an almost colorless flame. The oxygen may be tested 

179 























by thrusting into it a glowing splinter; the splinter will immediately burst into flame. Which 

gas is liberated more rapidly? . 

Fill a tumbler two-thirds full of sulphuric acid, 1 to 20. Slip the two copper strips into the 
battery stand and connect them in series with the cells. If the strips of copper are not 
bright and clean, they must be sand-papered. After the current has been flowing for a few 
minutes, lift the copper strips out of the acid and examine them. The oxygen unites with the 
copper at the anode to form copper oxide, which is black in color. What is the appearance 
of the other plate? . 


STORAGE CELLS 


Method. Fill the tumbler two-thirds full of a solution of sulphuric acid in water, one part 
of acid to 12 parts of water. Sand-paper the lead strips until they are bright and clean. Clamp 
them in position in the battery clamp and immerse them in the acid solution. Connect 

a voltmeter across the terminals. Does it show any 
difference of potential between the two strips? .... 

. Next connect the strips in 

series with two dry cells, or storage cells, an ammeter, 
and a rheostat as shown in Fig. 105. Adjust the 
rheostat so that about one ampere of current will 
flow through the circuit. Read the voltmeter and 
ammeter at 1 minute intervals for 5 minutes. Then 
lift the plates from the acid and examine them. If a 
brown coating is formed at the anode, disconnect the 
cells, the voltmeter, and the ammeter. If not, con¬ 
tinue to charge the storage cell for a few minutes 
more. The union of the oxygen with the lead plate 
at the anode forms lead dioxide, Pb 02 . 

Connect the cell you have just charged with an 
electric bell or a small motor until it is discharged. 
A voltmeter may be used, but it will discharge more 
slowly. Why? . The capac¬ 

ity of storage cells is rated in ampere-horns. What 

do you think the expression means? . 

. No 

hydrogen is set free when a storage cell is being 
discharged since it unites with the oxygen from the 
Fig. 105 dioxide plate to form water. 



180 





























Data. 


Time 

Voltmeter reading 

Ammeter reading 




















Questions. 1. Would you expect the specific weight of the electrolyte to rise or fall 
as a storage battery is being charged? Explain. 


2. Where were bubbles of gas liberated when the storage cell was being charged? 

3. Why were no oxygen bubbles liberated at the anode when the storage cell was being 
charged? 

4. How is the specific weight of the electrolyte in a storage cell affected as the cell is 
being discharged? What practical use can be made of this fact? 


181 













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Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE. 


EXP. 68 —ELECTRO-PLATING 


Purpose. (a) To show how an object may be plated with copper. 

(6) To find out how much copper one ampere of current will deposit per second. 

Apparatus: Two carbon rods, | in. diameter; copper strip, 3x4 in.; 2 dry cells or 2 storage cells; 

ammeter; rheostat; balance; weights; battery clamp; tumbler; copper sulphate 
solution; heavy copper wire. 

Note. In the note under Exp. 66 we learn that certain compounds in water solution 
dissociate into ions. Metallic salts dissociate into a positive metallic ion and a negative 
radical. When a current is passed through such a solution the metallic ion is attracted to the 
cathode, where the metal is deposited as its charge is neutralized. If the number of ions in 
close proximity to the cathode is kept uniform, then the metal will be deposited in an even 
layer. To keep the distribution of ions uniform, in commercial practice the electrolyte is 
agitated, either by stirring it, by blowing air through it, or by rotating either the anode or 
the cathode. Faraday found that the rate at which any metal is deposited by electrolysis is 
proportional to the time and to the strength of the current. Different metals are deposited 
at different rates. 

Method. Fasten two carbon rods in the clamp of a demonstration battery and immerse 
the lower ends of the rods in a tumbler one-half full of a nearly saturated solution of copper 
sulphate. Connect with at least two cells in series and pass the current through the solu¬ 
tion for from 3 to 5 minutes. Turn off the current and lift the rods from the solution. 
Is the copper deposited upon the anode or the cathode? .. 

Replace the carbon rods and reverse the direction of the current. Examine the rods 
again after about 5 minutes. Results? . 


Bend the sheet of copper into a cylinder so it will surround the anode. Weigh the 
cylinder, using a balance that is sensitive to hundredths of a gram. Use for the anode a 
heavy copper wire, preferably No. 9 or 10. Use the weighed cylinder as the cathode. Clamp 
both in position, and connect them in series with two cells, an ammeter, and a rheostat. 
Adjust the rheostat so that not more than 0.5 ampere of current is flowing through the 
circuit. The tumbler should be about two-thirds full of copper sulphate solution. Let the 
current flow for at least 30 minutes, keeping a record of the time. 

Remove the copper cylinder, rinse it with water, with alcohol, and then with ether. 

Dry it carefully at a low temperature. Is the coating of copper even and adherent? . 

. Weigh the copper cylinder. And the gain in weight, and then calculate 

the amount of copper that one ampere of current would deposit in one second. Compare 
your result with the accepted value. 


183 











Data. 


Time at beginning . 

Time at end of experiment . 

Number of seconds current is flowing . 

Strength of current used . 

Weight of cylinder in beginning . . . 

Weight of cylinder at end .. 

Gain in weight . ' . 

Gain in weight per second . 

Amount of copper that one ampere would deposit in one second . 

Accepted value . 

Questions and problems. 1. In electro-plating, why should the anode be made of the 
same metal as that with which the object is to be plated? 


2. How many grams of copper would be deposited by a current of 4 amperes in 10 
hours? 


3. State clearly how you would plate an object with silver. 


184 












Laboratory Exercises in Physics 
Chables E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 69 — ELECTROMAGNETIC INDUCTION 


Purpose. To show how a magnet may induce a current in a conductor moving through 
its magnetic field. 

Apparatus: Horseshoe magnet; primary spool of wire; secondary spool of wire; Daniell cell, or dry 
cell; key; galvanometer; No. 22 insulated copper wire. 

Note. In Exp. 62, we found that a current flowing through a conductor sets up a 
magnetic field. When the wire was wound into the form of a spiral or helix, such a coil was 
found to have polarity. The addition of an iron core to the helix 
gave us the electro-magnet. It is quite reasonable to suspect that a 
magnet will have some effect upon a conductor, since electricity and 
magnetism seem to be quite closely related. Faraday carried out a 
series of experiments in which he showed that electricity may be 
induced by means of a magnetic field. His discovery eventually led 
to the invention of the modern dynamo. 

Method, (a) Wind the No. 22 copper wire into a compact coil 
of about 40 turns approximately 1 in. in diameter. Fasten the ends 
of the coil to a sensitive galvanometer. Then thrust the coil down 
over the N-pole of the horseshoe magnet, as shown in Fig. 106. 

Is the galvanometer needle deflected? .. If 

. Does the galvanometer show any current 

flowing through the coil when it is held stationary, a little more than an inch from the end 
of the magnet? . Remove the coil quickly. Result? . 


(6) Repeat (a), using the other pole of the magnet. How do your results differ from 
those obtained in (a)? 

(c) Holding the coil stationary, thrust one pole of the magnet into the coil. Does it 
appear to matter whether the coil moves past the pole of the magnet or the magnet moves 

through the coil? . State concisely what conditions are needed to 

produce an induced current. 



sn. note the dirpptinn 


185 
























DYNAMO PRINCIPLE 


Wind 15 or 20 turns of wire, preferably No. 26 or No. 28, into a coil like that shown 
in Fig. 107. The oblong coil should be of such a size that it may be rotated between the 
poles of the magnet. Leave the ends at least 18 in. long and connect them to the galva¬ 
nometer. Tie the separate turns with thread in order to make a compact coil. Hold the 



Fig. 107 





end of the coil with the thumb and finger so that the coil is between the poles of the magnet 
as shown in Fig. 108.' Give the coil a sudden twist so that the upper half will move about 
60° past the N-pole of the magnet. Note the direction in which the galvanometer is deflected. 

. Continue to turn the coil until the wires {B) are nearly adjacent 

to the N-pole. Then give the coil a quick twist as the wires pass the N-pole. Note the 

deflection.Hold the coil so that its plane is at nearly right angles 

to the magnetic lines of force, and twist it through about 60° as before. Results?. 


Rotate the loop in the opposite direction and compare results. 


State concisely the conditions needed to produce an induced current by means of a 
rotating loop and a magnet. 


What advantage do you think an electro-magnet would have over a permanent magnet? 

. What advantage do you think two coils set at right angles to 

each other would have over a single coil? . 


186 






































INDUCTION BY VARYING FIELD 


Connect the primary coil of Fig. 109 in series with the cell and a contact key. The 
terminals of the secondary coil S should be connected to a sensitive galvanometer. Hold the 

primary coil with one-quarter of its length inserted in the sec¬ 
ondary coil. Watch the galvanometer closely as you close the 

contact key. Result? . 

Hold the key firmly closed for a few moments. Does the cur¬ 
rent continue to flow when the key is held? . 

. Break the circuit suddenly. What is the effect? 



Fig. 109 


Repeat the experiment when the primary is inserted in the 
secondal-y half its length, and again when it is inserted its entire 
length. How is the magnitude of the deflection affected? 


Repeat the experiment when an iron core is placed inside the primary coil. Results? 

Conclusion: State clearly as many ways of producing an induced current as jmu can. 
Tell upon what factors its strength and direction appear to depend. 


187 


















Laboratory Exercises in Physics 
Charles E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME 

DATE. 


EXP. 70 —ELECTRIC MOTOR 


Purpose. To study the principle of a simple electric motor. 

Apparatus: Demonstration motor, St. Louis type; dry cell or storage cell. 

Note. The electric motor consists essentially of three parts: the field magnet; the 
armature; and the commutator with brushes. The field magnet may consist of two perma¬ 
nent magnets with unhke poles adjacent. More often it is an 
electro-magnet. The armature is essentially an electro-magnet. 
The brushes rest on the commutator to carry current to or 
from the armature. The commutator changes the direction in 
which the current flows through the armature, thus reversing 
its polarity. This reversal occurs at such a time that the 
poles of the armature will be alternately attracted and repelled 
by the field magnet. The mutual attraction and repulsion 






between the poles of the field magnet and those of the armature produce the rotation of the 
armature. 

Method. Separate the bar magnets widely and connect the armature to the cell. With 
a bar magnet test the polarity of the armature in several different positions as you turn it 

189 




















































































slowly through a complete circle as shown in Fig. 110. Note that the polarity changes just as 
the brush shifts to a different segment of the commutator. Mark on the circle, of Fig. 110 the 
polarity of the armature in different positions. Of course both ends of the armature reverse 
polarity at the same instant. Next bring the bar magnets up to the position shown in 
Fig. 111. Explain fully why the armature rotates. What causes it to continue rotating 
when the poles of the armature and the field magnets are all in the same straight line?. . . 


Series wound motor. Replace the bar magnets with the electro-magnet. Connect the 
field magnet, the armature, and the cell all in series. See Fig. 112. Does the polarity of 

the field magnet change?.Make a sketch diagram (not a drawing) 

to show the passage of the current through a series wound motor. 

Shunt wound motor. Connect the cell with the motor in such a manner that the current 
will divide, part of it passing through the field magnet, and part through the armature. 
See Fig. 113. Make a sketch diagram to show how the current flows through such a motor. 



Series Wound Motor 


Shunt Wound Motor 







Laboratory Exercises in Physics , 
Chables E. Dull 

Copyright, 1923, by Henry Holt and Company 


NAME. 

DATE. 


EXP. 71 —MOTOR EFFICIENCY 


Purpose. To test the efficiency of a small direct current motor. The use of the Prony 
brake. 

Apparatus: Small series-wound motor, D. C., of at least | horsepower; starting rheostat; voltmeter, 
0-150; ammeter, 0-10; switch; Prony brake; spring balances, 20 or 25 lb. capacity; 
speed counter; stop watch. 

Note. The resistance of the armature of a motor is so small that it is likely to be burnt 
out unless a starting resistance is connected in series with it. See Fig. 114. Then as the 
motor comes up to speed, this resistance is gradually cut out. Of course the resistance of a 
motor armature at rest is the same as it is when the armature is rotating, but a motor develops 
a back E.M.F. when it is running. This opposes the direct E.M.F. which drives the motor, 
thus reducing the voltage and the amperage correspondingly. The faster the armature 
rotates, the higher the back E.M.F. For example, suppose a motor whose resistance is only 
5 ohms is connected to a 110-volt circuit. The current which will flow through the armature 
is 22 amperes. Suppose this motor when in operation develops a back E.M.F. of 100 volts. 
The effective voltage is only 10, and the current flowing through the armature is reduced to 
2 amperes. 



Method. Connect the motor in series with a starting resistance, a switch, and an 
ammeter. A voltmeter should be shunted across the terminals. Close the switch, and grad¬ 
ually cut out the resistance as the motor comes up to speed. When the resistance has all 
been cut out and the motor is running at full speed, read both meters. The product, volts 
times amperes, equals watts. This product gives us the input of the motor. One horsepower 
equals 746 watts, hence 1 watt is equivalent to 0.737 ft. lb. per second, or 44.22 ft. lb. per 
minute. 


191 











Arrange a Prony brake as shown in Fig. 115. A belt, canvas or leather, is looped around 
the pulley of the motor, and its ends fastened to the spring balances. (If the pulley is grooved, 
use a strong cord instead of the belt.) Measure the circumference of the pulley in feet by 
winding around it a few turns of fine copper wire and dividing the 
total length by the number of turns. The work done each revolution 
in overcoming friction is equal to the circumference of the pulley 
multiplied by the difference between the two balance readings. 
Adjust the tension of the balance so that the motor armature will 
make from 1200 to 1500 revolutions per minute. 

Students may be assigned as follows to secure the data. Student 
A holds the speedometer, which he has read carefully and holds in 
readiness to press against the center of the armature shaft when 
the experiment is started. Student B holds a stop watch, and a 
third student C takes the reading of the balances. He should take 
three or four readings of both balances during the minute the experi¬ 
ment is in progress and then find the average for each balance. 
Student D takes readings in a similar manner of the voltmeter and 
ammeter and finds the average. 

n\ When all is in readiness, student B says ‘^Go” and starts the 

\ stop watch. Student A presses the speed counter against the axis of 

' the armature, and the other two students begin to take readings of 

the balances and measuring instruments respectively. At the end of 
one minute, the time-keeper says “Stop.” The speed counter 
should be simultaneously removed, and the brake loosened. 



Fig. 115 


Repeat the experiment, first increasing the tension on the brake until the speed is reduced 
to about 600 or 800 revolutions per minute. 

If time permits, a third trial may be taken, using enough tension to reduce the speed to 
about 300 revolutions per minute. 


192 















Data. 


Without brake. 

Voltage, . 

Wattage, or input . 

Input in ft. lb. per minute. 
With brake, (output) 


Amperage, . 

equivalent to . ft. Ik. 

Horsepower of motor . 


Volts 

Amperes 

Watts 

Equivalent 
to ft. lb. 

Revolutions 
per minute 

Circum¬ 

ference 

Balance 

A 

Balance 

B 

Difference 
Pull on belt 

IVork done pet 
revolution 

Work done pet 
Tiinute(outpu1 

Efficiency 






































Calculations: 


193 


























APPENDIX A 


TABLES 


TABLE 1. —USEFUL NUMBERS 


12 

in. 


= 1 ft. 

3 

ft. 

= 1 yd. 

16§ 

ft. 


= 1 rd. 

320 

rd. 

= 1 mi. 

5280 

ft. 


= 1 mi. 

144 

sq. in. 

= 1 sq. ft. 

9 

sq. 

ft. 

= 1 sq. yd. 

1728 

cu. in. 

= 1 cu. ft. 

27 

cu. 

ft. 

= 1 cu. yd. 

2150.4 

cu. in. 

= 1 bu. 

231 

cu. 

in. 

= 1 gal. 

60 

mi. per hr. 

= 88 ft. per sec. 

1 

lb. 

avoir. 

= 7000 gr. 

1 

lb. Troy 

= 5760 gr. 

1 

oz. 

avoir. 

= 437.5 gr. 

1 

oz. Troy 

= 480 gr. 

1 

cu. 

ft. of water weighs 62.4 lb. 

TT* 


= 9.86965. 

erence 

of a 

circle 

= 27rr 

Area of circle 

= Trr*, or j T(P 

of sphere 


= 4 Trr^ 

Volume of sphere 

= 1 Trd^ 


TABLE 2. — METRIC-ENGLISH EQUIVALENTS 


1 

in. 

= 

2.5399 cm. 

1 

ft. 

= 

30.479 cm. 

1 

mi. 

= 

1609.3 m. * 

1 

mi. 

= 

1.6093 Km. 

1 

mm. 

= 

.03937 in. 

1 

cm. 

= 

.3937 in. 

1 

m. 

= 

39.3708 in. 

1 

m. 

= 

3.2809 ft. 

1 

m. 

= 

1.0936 yd. 

1 

sq. cm. 

= 

0.155 sq. in. 

1 

Km. 

= 

.62137 mi. 

1 

cu. in. 

= 

16.3862 c.c. 

1 

sq. in. 

= 

6.451 sq. cm. 

1 

Kgm. 

= 

2.2046 lb. 

1 

lb. 

= 

453.593 gm. 

1 

gm. 

= 

15.432 gr. 

1 

oz. 

= 

28.3495 gm. 

1 

1. 

= 

1.0567 qt. 


195 


TABLE 3. —SPECIFIC WEIGHT OF SOLIDS 


Aluminum.2.7 

Antimony .6.72 

Beeswax.0.96 

Brass.8.2-8.7 

Brick.1.6-2.0 

Bronze.8.7 

Butter .0.94 

Carbon .1.7-3.5 

Chestnut.0.61 

Cherry.0.71 

Coal, anthracite .... 1.26-1.8 

Coal, bituminous .... 1.26-1.4 

Copper .8.9 

Cork .0.24 

Diamond .3.53 

Elm.0.58 

Glass, crown.2.5 

Glass, flint.3.0-3.6 

Gold .19.3 

Gold, 18k.14.88 

Granite ..2.65 

Graphite.2.50 

Human Body .1.07 


Ice.0.917 

Iron, cast.7.1-7.6 

Iron, steel.7.79 

Iron, wrought.7.8-7.9 

Lead.11.34 

Lignum vitae.1.33 

Limestone.3.18 

Maple.0.755 

Magnesium.1.74 

Marble.2.7 

Oak.0.85 

Paraffin. 0.824-0.94 

Pine. 0.46-0.55 

Platinum.21.4 

Porcelain.2.38 

Quartz .2.65 

Silver .10.5 

Silver, sterling .10.38 

Sulphur.2.0 

Tallow .0.94 

Tin.7.0-7.3 

Tungsten.18.7 

Zinc.7.1 


TABLE 4. —SPECIFIC WEIGHT OF LIQUIDS 


Alcohol, grain. 

.... 0.794 

Mercury . 

. . . 13.56 

Alcohol, wood. 

.... 0.804 

Milk. 

. . . . 1.029 

Carbon bisulphide . . 

.... 1.27 

Nitric acid, 68 % . . . 

. . . . 1.41 

Carbon tetrachloride . . 

.... 1.60 

Oil, castor. 

. . . . 0.963 

Chloroform. 

.... 1.50 

Oil, cottonseed .... 

. . . . 0.924 

Ether. 

.... 0.72 

Oil, linseed. 

. . . . 0.94 

Gasoline. 

. 0.68-0.71 

Oil, ohve. 

. . . . 0.916 

Glycerin. 

.... 1.26 

Turpentine. 

. . . . 0.87 

Hydrochloric acid . . . 

.... 1.20 

Sulphuric acid .... 

. . . . 1.84 

Kerosene. 

. 0.778-0.804 

Water, sea . 

. . . . 1.026 


TABLE 5.— TENSILE STRENGTH 


Matebial 

Pounds per Square 
Inch 

Material 

Pounds per 
Square Inch 

Aluminum.... ... 

30,030-40,000 

50,000-150,000 

110,000-140,000 

60,000-70,000 

50,000-60,000 

80,000-120,000 

Iron, piano wire. 

357,000-390,000 

2600-3300 

50.000 

42,000 

80,000-330,000 

460,000 

Brass. 

Lead, drawn. 

Bronze wire, phosphor. 

Copper, drawn. 

Iron, annealed. 

Iron, hard drawn. 

Platinum, drawn .. 

Silver, drawn. 

Steel, ordinary . 

Steel, maximum. 


196 




















































































TABLE 6.— DENSITY OF DRY AIR. (GRAMS PER LITER) 


Temperature 





Pressure in 

Millimeters of Mercury 





710 

720 

730 

740 

750 

760 

770 

780 

10 ° c . 

1.165 

1 

182 

1 

198 

1 

215 

1 

231 

1 

247 

1 

.264 

1.280 

12 

1.157 

1 

173 

1 

190 

1 

206 

1 

222 

1 

239 

1 

.255 

1.271 

14 

1.149 

1 

165 

1 

181 

1 

198 

1 

214 

1 

230 

1 

246 

1.262 

16 

1.141 

1 

157 

1 

173 

1 

189 

1 

205 

1 

221 

1 

238 

1.253 

18 

1.133 

1 

149 

1 

165 

1 

181 

1 

197 

1 

213 

1 

229 

1.245 

20 

1.125 

1. 

141 

1. 

157 

1 

173 

1 

189 

1 

205 

1 

221 

1.236 

21 

1.121 

1. 

137 

1. 

153 

1. 

169 

1. 

185 

1. 

201 

1 

216 

1.232 

22 

1.118 

1. 

134 

1. 

149 

1. 

165 

1. 

181 

1. 

197 

1 

212 

1.228 

23 

1.114 

1. 

130 

1. 

145 

1. 

161 

1. 

177 

1. 

193 

1 

208 

1.224 

24 

1.110 

1. 

126 

1. 

142 

1. 

157 

1. 

173 

1. 

189 

1 

204 

1.220 

25 

1.103 

1. 

122 

1. 

138 

1. 

153 

1. 

169 

1. 

185 

1. 

200 

1.215 

26 

1.103 

1. 

118 

1. 

134 

1. 

149 

1. 

165 

1. 

181 

1. 

196 

1.211 

27 

1.099 

1. 

115 

1. 

130 

1. 

146 

1. 

161 

1. 

177 

1. 

192 

1.207 

28 

1.095 

1 

111 

1. 

126 

1. 

142 

1. 

157 

1. 

173 

1. 

188 

1.203 

30 

1.088 

1 

104 

1. 

119 

1. 

134 

1. 

149 

1. 

165 

1. 

180 

1.195 


TABLE 7.— CAPACITY OF AIR IN GRAINS OF WATER VAPOR PER CUBIC FOOT 


Degrees 

F. 

Grains per 
Cubic Foot 

Degrees 

F. 

Grains per 
Cubic Foot 

Degrees 

F. 

Grains per 
Cubic Foot 

Degrees 

F. 

Grains per 
Cubic Foot 

10 

.776 

46 

3.539 

66 

7.009 

86 

13.127 

20 

1.235 

48 

3.800 

68 

7.480 

88 

13.937 

30 

1.935 

50 

4.076 

70 

7.980 

90 

14.790 

32 

2.113 

52 

4..372 

72 

8.508 

92 

15.689 

34 

2.279 

54 

4.685 

74 

9.066 

94 

16.634 

36 

2.457 

56 

5.016 

76 

9.655 

96 

17.626 

38 

2.646 

58 

5.370 

78 

10.277 

98 

18.671 

40 

2.849 

60 

5.745 

80 

10.934 

100 

19.766 

42 

3.064 

62 

6.142 

82 

11.626 

102 

20.917 

44 

3.294 

64 

6.563 

84 

12.3.56 

104 

22.125 


197 

































































TABLE 8. — HYGROMETRY 


Diffekence between Dey and Wet-bulb Thermometers 


MOMETER, 
o jp 

1° 

2° 

3° 

4° 

5“ 

6° 

70 

8° 

9° 

10° 

11 ° 

12° 

13° 

14° 

15° 

50 

93 

87 

81 

74 

68 

62 

56 

50 

44 

39 

33 

28 

22 

17 

12 

52 

94 

88 

81 

75 

69 

63 

58 

52 

46 

41 

36 

30 

25 

20 

15 

54 

94 

88 

82 

76 

70 

65 

59 

54 

48 

43 

38 

33 

28 

23 

18 

56 

94 

88 

82 

77 

71 

66 

61 

55 

50 

45 

40 

35 

31 

26 

21 

58 

94 

89 

83 

77 

72 

67 

62 

57 

52 

47 

42 

38 

33 

28 

24 

60 

94 

89 

84 

78 

73 

68 

63 

58 

53 

49 

44 

40 

35 

31 

27 

62 

94 

89 

84 

79 

74 

69 

64 

60 

55 

50 

46 

41 

37 

33 

29 

64 

95 

90 

85 

79 

75 

70 

66 

61 

56 

52 

48 

43 

39 

35 

31 

66 

95 

90 

85 

80 

76 

71 

66 

62 

58 

53 

49 

45 

41 

37 

33 

68 

95 

90 

85 

81 

76 

72 

67 

63 

59 

55 

51 

47 

43 

39 

35 

70 

95 

90 

86 

81 

77 

72 

68 

64 

60 

56 

52 

48 

44 

40 

37 

72 

95 

91 

86 

82 

78 

73 

69 

65 

61 

57 

53 

49 

46 

42 

39 

74 

95 

91 

86 

82 

78 

74 

70 

66 

62 

58 

54 

51 

47 

44 

40 

76 

96 

91 

87 

83 

78 

74 

70 

67 

63 

59 

55 

52 

48 

45 

42 

78 

96 

91 

87 

83 

79 

75 

71 

67 

64 

60 

57 

53 

50 

46 

43 

80 

96 

91 

87 

83 

79 

76 

72 

68 

64 

61 

57 

54 

51 

47 

44 

84 

96 

92 

88 

84 

80 

77 

73 

70 

66 

63 

59 

56 

53 

50 

47 

88 

96 

92 

88 

85 

81 

78 

74 

71 

67 

64 

61 

58 

55 

52 

49 

90 

96 

92 

89 

85 

82 

78 

75 

72 

68 

64 

62 

58 

56 

53 

50 


TABLE 9.— VAPOR PRESSURE OF WATER IN MILLIMETERS OF MERCURY 


Degrees 

C. 

Millimeters 

Degrees 

C. 

Millimeters 

Degrees 

C. 

Millimeters 

0 

4.5 

23 

20.9 

60 

148.9 

5 

6.5 

24 

22.2 

70 

233.3 

10 

9.1 

25 

23.5 

80 

354.7 

15 

12.7 

26 

25.0 

85 

433.1 

16 

13.5 

27 

26.5 

90 

525.4 

17 

14.4 

28 

28.1 

95 

633.7 

18 

15.3 

29 

29.8 

96 

657.7 

19 

16.3 

30 

31.5 

97 

682.1 

20 

17.3 

35 

41.6 

98 

707.3 

21 

18.5 

40 

54.8 

99 

733.2 

22 

19.6 

50 

92.0 

100 

760. 


198 


















































TABLE 10. — COEFFICIENT OF LINEAR EXPANSION 


Coefficient of Linear Expansion. (1° Centigrade) 

Quartz.0000005 

Invar.0000009 

Glass.000009 

Platinum.000009 

Iron.000011 

Steel.000013 

Copper.000017 

Brass.000019 

Silver.000019 

Tin.000021 

Aluminum.000023 

Zinc. 000029 


TABLE 11. —HEAT CONSTANTS 


Name 

Specific 

Heat 

Melting 

Point 

Boiling 

Point 

Heat of 
Fusion 

Heat of Va¬ 
porization 

Alcohol. 

.65 

-130° C. 

78° C. 


205 

Aluminum. 

.217 

657 

2200 

76.8 

Ammonia. 


-75 

-33.5 

108 

295 

Brass. 

.09 

912 



Copper. 

.093 

1065 

2310 

42 


Glass. 

.198 




Ice. 

.5 

0 


80 


Iron. 

.113 

1550 

2450 

28 


Lead. 

.031 

327 

1525 

5.8 


Mercury. 

.033 

-39 

357 

2.8 


Platinum. 

.0323 

1760 


27.2 


Silver. 

.056 

961 

1952 

21. 


Tungsten. 

.0336 

3000 




Steam. 

.48 





Water. 

1.00 


100 


536 

Zinc. 

.093 

.419 

918 

28 


TABLE 12.— DENSITY OF WATER AT VARYING TEMPERATURES 


Degrees 

C. 

Grams per 

Cubic Centimeter 

Degrees 

C. 

Grams per 

Cubic Centimeter 

Degrees 

C. 

Grams per 

Cubic Centimeter 

0 

.99987 

15 

.99913 

60 

.98324 

1 

.99993 

20 

.99823 

65 

.98059 

2 

.99997 

25 

.99708 

70 

.97781 

3 

.99999 

30 

.99568 

75 

.97489 

4 

1.00000 

35 

.99406 

80 

.97183 

5 

.99999 

40 

.99225 

85 

.96865 

6 

.99998 

45 

.99025 

90 

.96534 

8 

.99987 

50 

.98807 

95 

.96192 

10 

.99973 

55 

.98573 

100 

.95838 


199 
























































































TABLE 13. —RELATIVE CONDUCTIVITY OF HEAT 


Silver. 100 

Copper. 92 

Aluminum. 48 

Zinc. 27 

Brass. 21-28 

Platinum. 17 

Iron. 12-15 

Steel. 6-11.7 

Lead. 8 


German silver. 7-8 

Mercury. 1.6 

Concrete. .22 

Glass.11-.23 

Sand, white. .09 

Asbestos. .04 

Soil, dry. . 033 

Firebrick.028 

Linen. .021 


Magnesia.016 

Paper.013 

Sawdust.012 

Wool.010 

Silk.0095 

Felt.0087 

Air.005 

Cotton wool.0043 


TABLE 14.— VELOCITY OF SOUND IN VARIOUS MEDIA. (APPROXIMATE) 


Material 

Feet per 

Second 

Air. 

1,089 

Aluminum. 

16,7.50 

Brass. 

11,.500 

Copper. 

12,000 

Glass. 

16,.500 

Hydrogen.. 

4,163 


Material 

Feet per 
■ Second 

Iron. 

16,500 

Steel. 

16,500 

Water, 4° C. 

4,590 

Water, 15° C. 

4,615 

Wood, along grain. 

14,300 

Wood, across grain. 

12,600 


TABLE 15. —INDEX OF REFRACTION 


Alcohol. 

... 1,36 

Diamond. 

. 2.47 

Olive oil. 

. 1.47 

Canada balsam. 

... 1.52 

Glass, crown. . . 

. 1.52 

Opal. 

. 1.45 

Cotton seed oil. 

... 1.47 

Glass, flint. 

. . 1.54-1.94 

Water. 

. 1.33 

Carbon disulphide. 

... 1.62 






200 








































































TABLE 16.— SPECIFIC RESISTANCE AND TEMPERATURE COEFFICIENT 


(From Timbie’s “Elements of Electricity”) 


Material (Commercial) 

Specific Resistance 

Ohms per Mil-Foot 

AT 20° C. 

Temperature 
Coefficient = 

Increase per degree C. 
Resistance at 0° C, 

Aluminum. 

17.4 

0.00435 

Copper, annealed. 

10.4 

0.0042 

Copper, hard drawn. 

10.65 


Iron, annealed. 

90. 

0.005 

Iron, E. B. B. (Roebling). 

64. 

0.0046 

German silver. 

114 to 275 

0.00025 

Manganin. 

250 to 450 

0.00001 

la la (Bowker), soft. 

283 

0.000005 

la la (Bowker), hard. 

300 

6.00001 

Advance (Driver-Harrisl. 

294 

0.00000 


TABLE 17. —SPECIFIC RESISTANCE 


Silver. 

Copper. . . 
Aluminum 
Platinum., 
Iron. 


9.74 

10.38 

17.4 

58.8 

64.0 


German silver 

Mercury. 

Nichrome.... 
Manganin.... 


125-196 

616.5 

747.4 

250-450 


201 






































TABLE 18. — PROPERTIES OF COPPER WIRE 


Gauge 

Number 

Diameter, 

Mils 

Ohms per 1000 
Feet at 0° C. 

Ohms per 1000 
Feet at 20° C. 

Feet per Ohm 

20° C. 

Capacity in 
Amperes 

0000 

460 

.04516 

.04901 

20,400 

312 

000 

409.6 

.05695 

.06180 

16,180 

262 

00 

364.8 

.07181 

.07793 

12,830 

220 

0 

324.9 

.09055 

.09827 

10,180 

185 

1 

289.3 

.1142 

.1239 

8,070 

156 

2 

257.6 

.1440 

.1563 

6,400 

131 

3 

229.4 

.1816 

.1970 

5,075 

110 

4 

204.3 

.2289 

.2485 

4,025 

92.3 

5 

181.9 

.2887 

.3133 

3,192 

77.6 

6 

162.0 

.3640 

.3951 

2,531 

65.2 

7 

144.3 

.4590 

.4982 

2,007 

54.8 

8 

128.5 

.5988 

.6282 

1,592 

46.1 

9 

114.4 

.7299 

.7921 

1,262 

38.7 

10 

101.9 

.9203 

.9989 

1,001 

32.5 

11 

90.74 

1.161 

1.260 

794.0 

27.3 

12 

80.81 

1.463 

1.588 

629.6 

23.0 

13 

71.96 

1.845 

2.003 

499.3 

19.3 

14 

64.08 

2.327 

2.525 

396.0 

16.2 

15 

57.07 

2.934 

3.184 

314.0 

13.6 

16 

50.82 

3.700 

4.016 

249.0 

11.5 

17 

45.26 

4.666 

5.064 

197.5 

9.6 

18 

40.30 

5.883 

6.385 

156.6 

8.1 

19 

35.89 

7.418 

8.051 

124.2 

6.7 

20 

31.96 

9.355 

10.15 

98.5 

5.7 

21 

28.45 

11.80 

12.80 

78.11 

4.8 

22 

25.35 

14.87 

16.14 

61.95 

4.0 

23 

22.57 

18.76 

20.36 

49.13 

3.4 

24 

20.10 

23.65 

25.67 

38.96 

2.8 

25 

17.90 

29.82 

32.37 

30.90 

2.4 

26 

15.94 

37.61 

40.81 

24.50 

2.0 

27 

14.20 

47.42 

51.47 

19.43 

1.7 

28 

12.64 

59.80 

64.90 

15.41 

1.4 

29 

11.26 

75.40 

81.83 

12.22 

1.2 

30 

10.03 

95.08 

103.2 

9.691 

1.0 

31 

8.928 

119.9 

130.1 

7.685 

0.84 

32 

7.950 

151.2 

164.1 

6.095 

0.70 

33 

7.08 

190.6 

206.9 

4.833 

0.60 

34 

6.305 

240.4 

260.9 

3.833 

0.50 

35 

5.615 

303.1 

329.0 

3.040 

0.42 

36 

5.000 

382.2 

414.8 

2.411 

0.35 

37 

4.453 

482.0 

523.1 

1.912 

0.27 

38 

3.965 

607.8 

659.6 

1.516 

0.25 

39 

3.531 

766.4 

831.8 

1.202 

0.21 

40 

3.145 

966.5 

1049. 

0.953 

0.17 


202 















TABLE 19.— NATURAL SINES AND TANGENTS 


Angle 

Sine 

Tangent 

Angle 

Sine 

Tangent 

Angle 

Sine 

Tangent 

0 

0.000 

0.000 

31 

0.515 

0.601 

62 

0.883 

1.881 

1 

0.017 

0.017 

32 

0.530 

0.625 

63 

0.891 

1.963 

2 

0.035 

0.035 

33 

0.545 

0.649 

64 

0.899 

2.050 

3 

0.052 

0.052 

34 

0.559 

0.675 

65 

0.906 

2.145 

4 

0.070 

0.070 

35 

0.574 

0.700 

66 

0.914 

2.246 

5 

0.087 

0.087 

36 

0.588 

0.727 

67 

0.921 

2.356 

6 

0.105 

0.105 

37 

0.602 

0.754 

68 

0.927 

2.475 

7 

0.122 

0.123 

38 

0.616 

0.781 

69 

0.934 

2.605 

8 

0.139 

0.141 

39 

0.629 

0.810 

70 

0.940 

2.747 

9 

0.158 

0.158 

40 

0.643 

0.839 

71 

0.946 

2.904 

10 

0.174 

0.176 

41 

0.656 

0.869 

72 

0.951 

3.07S 

11 

0.191 

0.194 

42 

0.669 

0.900 

73 

0.956 

3.271 

12 

0.208 

0.213 

43 

0.682 

0.933 

74 

0.961 

3.487 

13 

0.225 

0.231 

44 

0.695 

0.966 

75 

0.966 

3.732 

14 

0.242 

0.249 

45 

0.707 

1.000 

76 

0.970 

4.011 

15 

0.259 

0.268 

46 

0.719 

1.036 

77 

0.974 

4.331 

16 

0.276 

0.287 

47 

0.731 

1.072 

78 

0.978 

4.705 

17 

0.292 

0.306 

48 

0.743 

1.111 

79 

0.982 

5.145 

18 

0.309 

0.325 

49 

0.755 

1.150 

80 

0.985 

5.671 

19 

0.326 

0.344 

50 

0.766 

1.192 

81 

0.988 

6.314 

20 

0.342 

0.364 

51 

0.777 

1.235 

82 

0.990 

7.115 

21 

0.358 

0.384 

52 

0.788 

1.280 

83 

0.993 

8.144 

22 

0.375 

0.404 

53 

0.799 

1.327 

84 

0.995 

9.514 

23 

0.391 

0.424 

54 

0.809 

1.376 

85 

0.996 

11.43 

24 

0.407 

0.445 

55 

0.819 

1.428 

86 

0.998 

14.30 

25 

0.423 

0.466 

56 

0.829 

1.483 

87 

0.999 

19.08 

26 

0.438 

0.488 

57 

0.839 

1.540 

88 

0.999 

28.64 

27 

0.454 

0.510 

58 

0.848 

1.600 

89 

1.000 

57.29 

28 

0.469 

0.532 

59 

0.857 

1.664 

90 

1.000 

Infinity 

29 

0.485 

0.554 

60 

0.866 

1.732 




30 

0.500 

0.577 

61 

0.875 

1.804 





April, jg 23 

PRINTED IN THE U. S. A. 





























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